Copy of TwistWorksheet_ver2

325 days ago by Ben.LeVeque

K.<a> = NumberField(x^2-x-1);K 
        
Number Field in a with defining polynomial x^2 - x - 1
Number Field in a with defining polynomial x^2 - x - 1
E = EllipticCurve(K,[1,a+1,a,a,0]) 
       
list((E.a_invariants())) 
        
[1, a + 1, a, a, 0]
[1, a + 1, a, a, 0]
E.quadratic_twist(2).conductor().norm() 
        
126976
126976
f = open('/home/bleveque/matched1000.txt') 
       
def grabber(line): return eval('['+line.split('[')[1].split(']')[0]+']') 
       
####### ######### # Code to compute twists of curves of N<1000 from our original curve list. Computes # # twists by x+ya, where x and y range only between +-5. # # (note: "curve_num = 0" clearly in the wrong place!) # ####### ######### new_curve_list = [] for line in f.readlines(): curve_num = 0 print 'curve_num: ',curve_num E = EllipticCurve(K,grabber(line)) for i in range(-5,5): for j in range(-5,5): if i!=0 and j!=0: F = E.quadratic_twist(i+j*a).global_minimal_model() if F.conductor().norm() < 1001: new_ind = 1 g = open('/home/bleveque/matched1000ver2.txt') for s in g.readlines(): if F.is_isomorphic(EllipticCurve(K,grabber(s))): new_ind = 0 if new_ind: new_curve_list.append(F) print F.a_invariants() curve_num+=1 
        
WARNING: Output truncated!  
full_output.txt



curve_num:  0
(a + 1, -a, 0, 7*a - 23, -24*a + 20)
curve_num:  0
curve_num:  0
(a + 1, 1, 1, -5*a - 5, -17*a - 13)
curve_num:  0
curve_num:  0
curve_num:  0
(1, a - 1, 0, -a, -71*a - 44)
(a, -a - 1, 0, 0, -40*a - 25)
(a, a - 1, a + 1, -a, 3*a - 7)
(a + 1, a, a + 1, 0, -4*a - 3)
curve_num:  0
curve_num:  0
(a + 1, -1, a, -54*a - 33, -63*a - 39)
(a, a + 1, 0, -6*a - 4, -11*a - 6)
curve_num:  0
(a + 1, a - 1, a, 7*a - 12, -a + 2)
(1, 1, 0, -2, 7*a + 3)
curve_num:  0
(0, 1, 0, -96*a - 59, -246*a - 152)
(0, -a - 1, 0, -13*a - 8, 0)
(0, a + 1, 0, a, 0)
(0, 1, 0, 2*a - 3, 0)
(0, a + 1, 0, a, 0)
curve_num:  0
curve_num:  0
curve_num:  0
curve_num:  0
curve_num:  0
curve_num:  0
curve_num:  0
curve_num:  0
curve_num:  0
(0, -a, 0, -53*a - 33, -126*a - 78)
(0, a, 0, 7*a - 13, 6*a - 12)
(0, -a + 1, 0, -7*a - 6, -6*a - 6)
curve_num:  0
(a, -a - 1, a + 1, -73*a - 44, -308*a - 190)
curve_num:  0
curve_num:  0
curve_num:  0
(a, a, a + 1, 39*a + 24, 63*a + 39)
(a + 1, a, 0, 9*a - 9, -7*a + 15)
(1, a - 1, a + 1, 6*a + 2, 2*a + 3)
curve_num:  0
curve_num:  0
(1, -1, 1, 1, 43*a + 26)
curve_num:  0
(a + 1, 1, a + 1, 27*a + 17, 27*a + 17)
curve_num:  0
curve_num:  0
curve_num:  0
curve_num:  0
curve_num:  0
curve_num:  0
curve_num:  0
curve_num:  0
curve_num:  0

...

curve_num:  0
curve_num:  0
curve_num:  0
curve_num:  0
curve_num:  0
curve_num:  0
curve_num:  0
curve_num:  0
curve_num:  0
curve_num:  0
curve_num:  0
curve_num:  0
curve_num:  0
curve_num:  0
curve_num:  0
curve_num:  0
curve_num:  0
curve_num:  0
curve_num:  0
curve_num:  0
curve_num:  0
curve_num:  0
curve_num:  0
curve_num:  0
curve_num:  0
curve_num:  0
curve_num:  0
curve_num:  0
curve_num:  0
curve_num:  0
curve_num:  0
curve_num:  0
curve_num:  0
curve_num:  0
curve_num:  0
curve_num:  0
curve_num:  0
curve_num:  0
curve_num:  0
curve_num:  0
(0, -a, 1, -42*a - 53, -192*a - 140)
curve_num:  0
curve_num:  0
curve_num:  0
curve_num:  0
curve_num:  0
curve_num:  0
curve_num:  0
curve_num:  0
curve_num:  0
curve_num:  0
curve_num:  0
curve_num:  0
curve_num:  0
curve_num:  0
curve_num:  0
curve_num:  0
curve_num:  0
curve_num:  0
curve_num:  0
WARNING: Output truncated!  
full_output.txt



curve_num:  0
(a + 1, -a, 0, 7*a - 23, -24*a + 20)
curve_num:  0
curve_num:  0
(a + 1, 1, 1, -5*a - 5, -17*a - 13)
curve_num:  0
curve_num:  0
curve_num:  0
(1, a - 1, 0, -a, -71*a - 44)
(a, -a - 1, 0, 0, -40*a - 25)
(a, a - 1, a + 1, -a, 3*a - 7)
(a + 1, a, a + 1, 0, -4*a - 3)
curve_num:  0
curve_num:  0
(a + 1, -1, a, -54*a - 33, -63*a - 39)
(a, a + 1, 0, -6*a - 4, -11*a - 6)
curve_num:  0
(a + 1, a - 1, a, 7*a - 12, -a + 2)
(1, 1, 0, -2, 7*a + 3)
curve_num:  0
(0, 1, 0, -96*a - 59, -246*a - 152)
(0, -a - 1, 0, -13*a - 8, 0)
(0, a + 1, 0, a, 0)
(0, 1, 0, 2*a - 3, 0)
(0, a + 1, 0, a, 0)
curve_num:  0
curve_num:  0
curve_num:  0
curve_num:  0
curve_num:  0
curve_num:  0
curve_num:  0
curve_num:  0
curve_num:  0
(0, -a, 0, -53*a - 33, -126*a - 78)
(0, a, 0, 7*a - 13, 6*a - 12)
(0, -a + 1, 0, -7*a - 6, -6*a - 6)
curve_num:  0
(a, -a - 1, a + 1, -73*a - 44, -308*a - 190)
curve_num:  0
curve_num:  0
curve_num:  0
(a, a, a + 1, 39*a + 24, 63*a + 39)
(a + 1, a, 0, 9*a - 9, -7*a + 15)
(1, a - 1, a + 1, 6*a + 2, 2*a + 3)
curve_num:  0
curve_num:  0
(1, -1, 1, 1, 43*a + 26)
curve_num:  0
(a + 1, 1, a + 1, 27*a + 17, 27*a + 17)
curve_num:  0
curve_num:  0
curve_num:  0
curve_num:  0
curve_num:  0
curve_num:  0
curve_num:  0
curve_num:  0
curve_num:  0

...

curve_num:  0
curve_num:  0
curve_num:  0
curve_num:  0
curve_num:  0
curve_num:  0
curve_num:  0
curve_num:  0
curve_num:  0
curve_num:  0
curve_num:  0
curve_num:  0
curve_num:  0
curve_num:  0
curve_num:  0
curve_num:  0
curve_num:  0
curve_num:  0
curve_num:  0
curve_num:  0
curve_num:  0
curve_num:  0
curve_num:  0
curve_num:  0
curve_num:  0
curve_num:  0
curve_num:  0
curve_num:  0
curve_num:  0
curve_num:  0
curve_num:  0
curve_num:  0
curve_num:  0
curve_num:  0
curve_num:  0
curve_num:  0
curve_num:  0
curve_num:  0
curve_num:  0
curve_num:  0
(0, -a, 1, -42*a - 53, -192*a - 140)
curve_num:  0
curve_num:  0
curve_num:  0
curve_num:  0
curve_num:  0
curve_num:  0
curve_num:  0
curve_num:  0
curve_num:  0
curve_num:  0
curve_num:  0
curve_num:  0
curve_num:  0
curve_num:  0
curve_num:  0
curve_num:  0
curve_num:  0
curve_num:  0
curve_num:  0
 
       
hr = open('/home/bleveque/twists.txt') 
       
h.readline() 
        
'(a + 1, 1, 1, -5*a - 5, -17*a - 13)\n'
'(a + 1, 1, 1, -5*a - 5, -17*a - 13)\n'
# This just adds the lines from the output of the last code which start with '(' (i.e. are new curves) to a file hw = open('/home/bleveque/condensedtwists.txt','w') for line in hr.readlines(): if line[0] == '(': hw.write(line) hr.close() hw.close() 
       
file1 = open('/home/bleveque/condensedtwists.txt') 
       
EllipticCurve(K,eval('['+file1.readline().split('\n')[0].split('(')[1].split(')')[0]+']')) 
        
Elliptic Curve defined by y^2 = x^3 + x^2 + (-96*a-59)*x + (-246*a-152)
over Number Field in a with defining polynomial x^2 - x - 1
Elliptic Curve defined by y^2 = x^3 + x^2 + (-96*a-59)*x + (-246*a-152) over Number Field in a with defining polynomial x^2 - x - 1
matchedfile = open('/home/bleveque/matched.txt') 
       
######## # This code is to double check that the curves produced aren't isomorphic to those in the list, and also to # check if any are in the isogeny classes of those curves. It will have to be checked if any are isogenous # to each other. ######## for line in file1.readlines(): E = EllipticCurve(K,eval('['+line.split('\n')[0].split('(')[1].split(')')[0]+']')) print 'current curve: ', E.a_invariants() matchedfile = open('/home/bleveque/matched1000.txt') for s in matchedfile.readlines(): F = EllipticCurve(K,grabber(s)) if E.is_isomorphic(F): print 'curve: ', E.a_invariants(), 'is isomorphic to curve: ', F.a_invariants() try: if E.is_isogenous(F): print 'curve: ', E.a_invariants(), 'is isogenous to curve: ', F.a_invariants() except NotImplementedError: print E.a_invariants(), 'seems to be isogenous to ', F.a_invariants(), 'but no isogeny constructed' 
        
WARNING: Output truncated!  
full_output.txt



current curve:  (a + 1, -a, 0, 7*a - 23, -24*a + 20)
current curve:  (a + 1, 1, 1, -5*a - 5, -17*a - 13)
current curve:  (1, a - 1, 0, -a, -71*a - 44)
current curve:  (a, -a - 1, 0, 0, -40*a - 25)
current curve:  (a, a - 1, a + 1, -a, 3*a - 7)
current curve:  (a + 1, a, a + 1, 0, -4*a - 3)
current curve:  (a + 1, -1, a, -54*a - 33, -63*a - 39)
current curve:  (a, a + 1, 0, -6*a - 4, -11*a - 6)
current curve:  (a + 1, a - 1, a, 7*a - 12, -a + 2)
current curve:  (1, 1, 0, -2, 7*a + 3)
current curve:  (0, 1, 0, -96*a - 59, -246*a - 152)
curve:  (0, 1, 0, -96*a - 59, -246*a - 152) is isogenous to curve:  (0,
a + 1, 0, a - 5, 3*a - 4)
current curve:  (0, -a - 1, 0, -13*a - 8, 0)
curve:  (0, -a - 1, 0, -13*a - 8, 0) is isogenous to curve:  (0, a + 1,
0, a - 5, 3*a - 4)
current curve:  (0, a + 1, 0, a, 0)
curve:  (0, a + 1, 0, a, 0) is isogenous to curve:  (0, a + 1, 0, a - 5,
3*a - 4)
current curve:  (0, 1, 0, 2*a - 3, 0)
curve:  (0, 1, 0, 2*a - 3, 0) is isogenous to curve:  (0, a + 1, 0, a -
5, 3*a - 4)
current curve:  (0, a + 1, 0, a, 0)
curve:  (0, a + 1, 0, a, 0) is isogenous to curve:  (0, a + 1, 0, a - 5,
3*a - 4)
current curve:  (0, -a, 0, -53*a - 33, -126*a - 78)
current curve:  (0, a, 0, 7*a - 13, 6*a - 12)
current curve:  (0, -a + 1, 0, -7*a - 6, -6*a - 6)
current curve:  (a, -a - 1, a + 1, -73*a - 44, -308*a - 190)
(a, -a - 1, a + 1, -73*a - 44, -308*a - 190) seems to be isogenous to 
(1, -1, a, -2*a, a) but no isogeny constructed
current curve:  (a, a, a + 1, 39*a + 24, 63*a + 39)
current curve:  (a + 1, a, 0, 9*a - 9, -7*a + 15)
current curve:  (1, a - 1, a + 1, 6*a + 2, 2*a + 3)
current curve:  (1, -1, 1, 1, 43*a + 26)
current curve:  (a + 1, 1, a + 1, 27*a + 17, 27*a + 17)
current curve:  (1, -a, 1, -734*a - 454, -11114*a - 6869)
current curve:  (a, 1, 0, -13*a - 13, -56*a - 8)
current curve:  (a + 1, a + 1, 0, -104*a - 65, -792*a - 488)
current curve:  (1, -a - 1, 1, 60*a + 37, -855*a - 529)
current curve:  (a, -1, 1, -8*a + 15, 45*a - 79)
current curve:  (a + 1, -a - 1, 1, 7*a + 7, -45*a - 34)
current curve:  (0, -a, 1, 67*a + 42, -1426*a - 882)
curve:  (0, -a, 1, 67*a + 42, -1426*a - 882) is isogenous to curve:  (0,
-a + 1, 1, -2*a - 1, 2*a + 1)
current curve:  (0, a, 1, -8*a + 17, 76*a - 131)
curve:  (0, a, 1, -8*a + 17, 76*a - 131) is isogenous to curve:  (0, -a
+ 1, 1, -2*a - 1, 2*a + 1)
current curve:  (0, -a + 1, 1, 8*a + 9, -76*a - 55)
curve:  (0, -a + 1, 1, 8*a + 9, -76*a - 55) is isogenous to curve:  (0,
-a + 1, 1, -2*a - 1, 2*a + 1)
current curve:  (0, 1, 1, -175*a - 108, -1425*a - 881)
curve:  (0, 1, 1, -175*a - 108, -1425*a - 881) is isogenous to curve: 
(0, 1, 1, 2, 4)
current curve:  (0, -1, 1, -8, -7)
curve:  (0, -1, 1, -8, -7) is isogenous to curve:  (0, 1, 1, 2, 4)
current curve:  (0, -a - 1, 1, -24*a - 16, -54*a - 34)
curve:  (0, -a - 1, 1, -24*a - 16, -54*a - 34) is isogenous to curve: 
(0, 1, 1, 2, 4)
current curve:  (0, -1, 0, -2*a - 1, 0)
curve:  (0, -1, 0, -2*a - 1, 0) is isogenous to curve:  (0, a + 1, 0, a
- 5, 3*a - 4)
current curve:  (0, -a - 1, 0, 15*a - 22, -14*a + 22)
curve:  (0, -a - 1, 0, 15*a - 22, -14*a + 22) is isogenous to curve: 
(0, a + 1, 0, a - 5, 3*a - 4)
current curve:  (0, -1, 0, -2*a - 1, 0)
curve:  (0, -1, 0, -2*a - 1, 0) is isogenous to curve:  (0, a + 1, 0, a
- 5, 3*a - 4)
current curve:  (0, -a - 1, 0, -13*a - 8, 0)
curve:  (0, -a - 1, 0, -13*a - 8, 0) is isogenous to curve:  (0, a + 1,
0, a - 5, 3*a - 4)
current curve:  (0, 1, 0, 2*a - 3, 0)
curve:  (0, 1, 0, 2*a - 3, 0) is isogenous to curve:  (0, a + 1, 0, a -
5, 3*a - 4)
current curve:  (0, -1, 0, -2*a - 1, 0)

...

current curve:  (0, -a, 0, -45*a - 28, 199*a + 123)
curve:  (0, -a, 0, -45*a - 28, 199*a + 123) is isogenous to curve:  (0,
a, 0, a - 1, 0)
current curve:  (0, -a + 1, 0, 45*a - 73, 199*a - 322)
curve:  (0, -a + 1, 0, 45*a - 73, 199*a - 322) is isogenous to curve: 
(0, a - 1, 0, -a, 0)
current curve:  (0, -a, 0, 6*a - 11, 11*a - 18)
curve:  (0, -a, 0, 6*a - 11, 11*a - 18) is isogenous to curve:  (0, a -
1, 0, -a, 0)
current curve:  (0, 1, 0, 2*a - 3, 0)
curve:  (0, 1, 0, 2*a - 3, 0) is isogenous to curve:  (0, a + 1, 0, a -
5, 3*a - 4)
current curve:  (0, -a - 1, 0, 15*a - 22, -14*a + 22)
curve:  (0, -a - 1, 0, 15*a - 22, -14*a + 22) is isogenous to curve: 
(0, a + 1, 0, a - 5, 3*a - 4)
current curve:  (0, 1, 0, 2*a - 3, 0)
curve:  (0, 1, 0, 2*a - 3, 0) is isogenous to curve:  (0, a + 1, 0, a -
5, 3*a - 4)
current curve:  (0, -1, 0, -2*a - 1, 0)
curve:  (0, -1, 0, -2*a - 1, 0) is isogenous to curve:  (0, a + 1, 0, a
- 5, 3*a - 4)
current curve:  (0, a + 1, a + 1, 6*a - 30, 42*a - 49)
current curve:  (0, -a - 1, a, -4*a - 25, -38*a + 19)
current curve:  (a + 1, -a + 1, 1, -15*a - 9, -69*a - 43)
current curve:  (1, a - 1, 0, 9*a - 15, -a + 1)
current curve:  (a, a, 0, -3, -5*a - 3)
current curve:  (a, a - 1, a + 1, -66*a - 40, -92*a - 57)
current curve:  (a + 1, a + 1, 1, 3*a - 3, 3*a - 7)
current curve:  (1, -a, 0, -9*a - 6, a)
current curve:  (a + 1, -a, 1, -61*a - 38, -524*a - 324)
current curve:  (a, -a + 1, 1, -9*a - 6, -30*a - 17)
current curve:  (a + 1, 0, 1, 8*a - 15, 30*a - 47)
current curve:  (1, -a + 1, a + 1, -5*a - 5, 23*a + 9)
current curve:  (1, -a, 0, -61*a - 38, 81*a + 52)
current curve:  (a + 1, a + 1, 1, -5*a - 7, -25*a + 21)
current curve:  (a, a, 0, 8*a - 15, 11*a + 17)
current curve:  (a + 1, -a + 1, 1, -11*a - 9, 295*a + 181)
current curve:  (0, a, a + 1, -223*a - 138, -2071*a - 1280)
current curve:  (0, -a, a + 1, 2*a - 13, 7*a - 21)
current curve:  (0, a - 1, a + 1, -32*a - 21, -116*a - 72)
current curve:  (0, a, a, -43*a - 28, -203*a - 126)
current curve:  (0, -a, a, 32*a - 53, 115*a - 187)
current curve:  (0, a - 1, a, -2*a - 11, -8*a - 13)
current curve:  (a, -a - 1, a + 1, -19*a - 17, -38*a - 28)
curve:  (a, -a - 1, a + 1, -19*a - 17, -38*a - 28) is isogenous to
curve:  (a, -a - 1, a + 1, -4*a - 2, 5*a + 3)
current curve:  (a, -a - 1, a, -113*a - 71, -645*a - 399)
curve:  (a, -a - 1, a, -113*a - 71, -645*a - 399) is isogenous to curve:
(1, -1, a, a, -a)
current curve:  (0, 0, 1, 0, -54*a - 34)
curve:  (0, 0, 1, 0, -54*a - 34) is isogenous to curve:  (0, 0, 1, 0, 0)
current curve:  (0, 0, a + 1, 0, -21*a - 14)
curve:  (0, 0, a + 1, 0, -21*a - 14) is isogenous to curve:  (0, 0, a +
1, 0, -a)
current curve:  (a + 1, 1, 0, -210*a - 129, -1942*a - 1200)
curve:  (a + 1, 1, 0, -210*a - 129, -1942*a - 1200) is isogenous to
curve:  (1, -1, a, a - 3, -2*a + 3)
current curve:  (a, -a - 1, a + 1, 62*a + 37, 43*a + 26)
curve:  (a, -a - 1, a + 1, 62*a + 37, 43*a + 26) is isogenous to curve: 
(1, -1, a + 1, -2*a - 2, a + 1)
current curve:  (0, 0, a, 0, -142*a - 88)
curve:  (0, 0, a, 0, -142*a - 88) is isogenous to curve:  (0, 0, a, 0,
0)
current curve:  (0, 1, a + 1, -30*a - 18, 8*a + 5)
current curve:  (0, -1, a + 1, -5*a + 7, 3*a - 6)
current curve:  (0, -a - 1, a + 1, -4*a - 1, 4*a + 2)
current curve:  (0, -a, a, -133*a - 83, -820*a - 507)
current curve:  (0, a, a, 17*a - 33, -18*a + 19)
current curve:  (0, -a + 1, a, -17*a - 16, -45*a - 30)
current curve:  (0, -a, a + 1, -133*a - 83, 242*a + 149)
current curve:  (0, a, a + 1, 17*a - 33, 44*a - 75)
current curve:  (0, -a + 1, a + 1, -17*a - 16, 17*a + 1)
current curve:  (0, -a, 1, -42*a - 53, -192*a - 140)
WARNING: Output truncated!  
full_output.txt



current curve:  (a + 1, -a, 0, 7*a - 23, -24*a + 20)
current curve:  (a + 1, 1, 1, -5*a - 5, -17*a - 13)
current curve:  (1, a - 1, 0, -a, -71*a - 44)
current curve:  (a, -a - 1, 0, 0, -40*a - 25)
current curve:  (a, a - 1, a + 1, -a, 3*a - 7)
current curve:  (a + 1, a, a + 1, 0, -4*a - 3)
current curve:  (a + 1, -1, a, -54*a - 33, -63*a - 39)
current curve:  (a, a + 1, 0, -6*a - 4, -11*a - 6)
current curve:  (a + 1, a - 1, a, 7*a - 12, -a + 2)
current curve:  (1, 1, 0, -2, 7*a + 3)
current curve:  (0, 1, 0, -96*a - 59, -246*a - 152)
curve:  (0, 1, 0, -96*a - 59, -246*a - 152) is isogenous to curve:  (0, a + 1, 0, a - 5, 3*a - 4)
current curve:  (0, -a - 1, 0, -13*a - 8, 0)
curve:  (0, -a - 1, 0, -13*a - 8, 0) is isogenous to curve:  (0, a + 1, 0, a - 5, 3*a - 4)
current curve:  (0, a + 1, 0, a, 0)
curve:  (0, a + 1, 0, a, 0) is isogenous to curve:  (0, a + 1, 0, a - 5, 3*a - 4)
current curve:  (0, 1, 0, 2*a - 3, 0)
curve:  (0, 1, 0, 2*a - 3, 0) is isogenous to curve:  (0, a + 1, 0, a - 5, 3*a - 4)
current curve:  (0, a + 1, 0, a, 0)
curve:  (0, a + 1, 0, a, 0) is isogenous to curve:  (0, a + 1, 0, a - 5, 3*a - 4)
current curve:  (0, -a, 0, -53*a - 33, -126*a - 78)
current curve:  (0, a, 0, 7*a - 13, 6*a - 12)
current curve:  (0, -a + 1, 0, -7*a - 6, -6*a - 6)
current curve:  (a, -a - 1, a + 1, -73*a - 44, -308*a - 190)
(a, -a - 1, a + 1, -73*a - 44, -308*a - 190) seems to be isogenous to  (1, -1, a, -2*a, a) but no isogeny constructed
current curve:  (a, a, a + 1, 39*a + 24, 63*a + 39)
current curve:  (a + 1, a, 0, 9*a - 9, -7*a + 15)
current curve:  (1, a - 1, a + 1, 6*a + 2, 2*a + 3)
current curve:  (1, -1, 1, 1, 43*a + 26)
current curve:  (a + 1, 1, a + 1, 27*a + 17, 27*a + 17)
current curve:  (1, -a, 1, -734*a - 454, -11114*a - 6869)
current curve:  (a, 1, 0, -13*a - 13, -56*a - 8)
current curve:  (a + 1, a + 1, 0, -104*a - 65, -792*a - 488)
current curve:  (1, -a - 1, 1, 60*a + 37, -855*a - 529)
current curve:  (a, -1, 1, -8*a + 15, 45*a - 79)
current curve:  (a + 1, -a - 1, 1, 7*a + 7, -45*a - 34)
current curve:  (0, -a, 1, 67*a + 42, -1426*a - 882)
curve:  (0, -a, 1, 67*a + 42, -1426*a - 882) is isogenous to curve:  (0, -a + 1, 1, -2*a - 1, 2*a + 1)
current curve:  (0, a, 1, -8*a + 17, 76*a - 131)
curve:  (0, a, 1, -8*a + 17, 76*a - 131) is isogenous to curve:  (0, -a + 1, 1, -2*a - 1, 2*a + 1)
current curve:  (0, -a + 1, 1, 8*a + 9, -76*a - 55)
curve:  (0, -a + 1, 1, 8*a + 9, -76*a - 55) is isogenous to curve:  (0, -a + 1, 1, -2*a - 1, 2*a + 1)
current curve:  (0, 1, 1, -175*a - 108, -1425*a - 881)
curve:  (0, 1, 1, -175*a - 108, -1425*a - 881) is isogenous to curve:  (0, 1, 1, 2, 4)
current curve:  (0, -1, 1, -8, -7)
curve:  (0, -1, 1, -8, -7) is isogenous to curve:  (0, 1, 1, 2, 4)
current curve:  (0, -a - 1, 1, -24*a - 16, -54*a - 34)
curve:  (0, -a - 1, 1, -24*a - 16, -54*a - 34) is isogenous to curve:  (0, 1, 1, 2, 4)
current curve:  (0, -1, 0, -2*a - 1, 0)
curve:  (0, -1, 0, -2*a - 1, 0) is isogenous to curve:  (0, a + 1, 0, a - 5, 3*a - 4)
current curve:  (0, -a - 1, 0, 15*a - 22, -14*a + 22)
curve:  (0, -a - 1, 0, 15*a - 22, -14*a + 22) is isogenous to curve:  (0, a + 1, 0, a - 5, 3*a - 4)
current curve:  (0, -1, 0, -2*a - 1, 0)
curve:  (0, -1, 0, -2*a - 1, 0) is isogenous to curve:  (0, a + 1, 0, a - 5, 3*a - 4)
current curve:  (0, -a - 1, 0, -13*a - 8, 0)
curve:  (0, -a - 1, 0, -13*a - 8, 0) is isogenous to curve:  (0, a + 1, 0, a - 5, 3*a - 4)
current curve:  (0, 1, 0, 2*a - 3, 0)
curve:  (0, 1, 0, 2*a - 3, 0) is isogenous to curve:  (0, a + 1, 0, a - 5, 3*a - 4)
current curve:  (0, -1, 0, -2*a - 1, 0)

...

current curve:  (0, -a, 0, -45*a - 28, 199*a + 123)
curve:  (0, -a, 0, -45*a - 28, 199*a + 123) is isogenous to curve:  (0, a, 0, a - 1, 0)
current curve:  (0, -a + 1, 0, 45*a - 73, 199*a - 322)
curve:  (0, -a + 1, 0, 45*a - 73, 199*a - 322) is isogenous to curve:  (0, a - 1, 0, -a, 0)
current curve:  (0, -a, 0, 6*a - 11, 11*a - 18)
curve:  (0, -a, 0, 6*a - 11, 11*a - 18) is isogenous to curve:  (0, a - 1, 0, -a, 0)
current curve:  (0, 1, 0, 2*a - 3, 0)
curve:  (0, 1, 0, 2*a - 3, 0) is isogenous to curve:  (0, a + 1, 0, a - 5, 3*a - 4)
current curve:  (0, -a - 1, 0, 15*a - 22, -14*a + 22)
curve:  (0, -a - 1, 0, 15*a - 22, -14*a + 22) is isogenous to curve:  (0, a + 1, 0, a - 5, 3*a - 4)
current curve:  (0, 1, 0, 2*a - 3, 0)
curve:  (0, 1, 0, 2*a - 3, 0) is isogenous to curve:  (0, a + 1, 0, a - 5, 3*a - 4)
current curve:  (0, -1, 0, -2*a - 1, 0)
curve:  (0, -1, 0, -2*a - 1, 0) is isogenous to curve:  (0, a + 1, 0, a - 5, 3*a - 4)
current curve:  (0, a + 1, a + 1, 6*a - 30, 42*a - 49)
current curve:  (0, -a - 1, a, -4*a - 25, -38*a + 19)
current curve:  (a + 1, -a + 1, 1, -15*a - 9, -69*a - 43)
current curve:  (1, a - 1, 0, 9*a - 15, -a + 1)
current curve:  (a, a, 0, -3, -5*a - 3)
current curve:  (a, a - 1, a + 1, -66*a - 40, -92*a - 57)
current curve:  (a + 1, a + 1, 1, 3*a - 3, 3*a - 7)
current curve:  (1, -a, 0, -9*a - 6, a)
current curve:  (a + 1, -a, 1, -61*a - 38, -524*a - 324)
current curve:  (a, -a + 1, 1, -9*a - 6, -30*a - 17)
current curve:  (a + 1, 0, 1, 8*a - 15, 30*a - 47)
current curve:  (1, -a + 1, a + 1, -5*a - 5, 23*a + 9)
current curve:  (1, -a, 0, -61*a - 38, 81*a + 52)
current curve:  (a + 1, a + 1, 1, -5*a - 7, -25*a + 21)
current curve:  (a, a, 0, 8*a - 15, 11*a + 17)
current curve:  (a + 1, -a + 1, 1, -11*a - 9, 295*a + 181)
current curve:  (0, a, a + 1, -223*a - 138, -2071*a - 1280)
current curve:  (0, -a, a + 1, 2*a - 13, 7*a - 21)
current curve:  (0, a - 1, a + 1, -32*a - 21, -116*a - 72)
current curve:  (0, a, a, -43*a - 28, -203*a - 126)
current curve:  (0, -a, a, 32*a - 53, 115*a - 187)
current curve:  (0, a - 1, a, -2*a - 11, -8*a - 13)
current curve:  (a, -a - 1, a + 1, -19*a - 17, -38*a - 28)
curve:  (a, -a - 1, a + 1, -19*a - 17, -38*a - 28) is isogenous to curve:  (a, -a - 1, a + 1, -4*a - 2, 5*a + 3)
current curve:  (a, -a - 1, a, -113*a - 71, -645*a - 399)
curve:  (a, -a - 1, a, -113*a - 71, -645*a - 399) is isogenous to curve:  (1, -1, a, a, -a)
current curve:  (0, 0, 1, 0, -54*a - 34)
curve:  (0, 0, 1, 0, -54*a - 34) is isogenous to curve:  (0, 0, 1, 0, 0)
current curve:  (0, 0, a + 1, 0, -21*a - 14)
curve:  (0, 0, a + 1, 0, -21*a - 14) is isogenous to curve:  (0, 0, a + 1, 0, -a)
current curve:  (a + 1, 1, 0, -210*a - 129, -1942*a - 1200)
curve:  (a + 1, 1, 0, -210*a - 129, -1942*a - 1200) is isogenous to curve:  (1, -1, a, a - 3, -2*a + 3)
current curve:  (a, -a - 1, a + 1, 62*a + 37, 43*a + 26)
curve:  (a, -a - 1, a + 1, 62*a + 37, 43*a + 26) is isogenous to curve:  (1, -1, a + 1, -2*a - 2, a + 1)
current curve:  (0, 0, a, 0, -142*a - 88)
curve:  (0, 0, a, 0, -142*a - 88) is isogenous to curve:  (0, 0, a, 0, 0)
current curve:  (0, 1, a + 1, -30*a - 18, 8*a + 5)
current curve:  (0, -1, a + 1, -5*a + 7, 3*a - 6)
current curve:  (0, -a - 1, a + 1, -4*a - 1, 4*a + 2)
current curve:  (0, -a, a, -133*a - 83, -820*a - 507)
current curve:  (0, a, a, 17*a - 33, -18*a + 19)
current curve:  (0, -a + 1, a, -17*a - 16, -45*a - 30)
current curve:  (0, -a, a + 1, -133*a - 83, 242*a + 149)
current curve:  (0, a, a + 1, 17*a - 33, 44*a - 75)
current curve:  (0, -a + 1, a + 1, -17*a - 16, 17*a + 1)
current curve:  (0, -a, 1, -42*a - 53, -192*a - 140)
#### # This code adds all of the curves that do not appear to be isogenous to known curves to a list to be written # to a file. #### newfile = open('/home/bleveque/newandisogenous.txt') newfile.readline() new_curve_data = [] for line in newfile.readlines(): if line[3] == 'r' or line[0] == '(': new_curve_data.append('['+line.split('(')[1].split(')')[0].replace(' ','')+']') else: new_curve_data = new_curve_data[:-1] newfile.close() newfilewrite = open('/home/bleveque/prelimnewcurvelist.txt','w') newfilewrite.write('N a-invariants \n') for data in new_curve_data: newfilewrite.write(str(EllipticCurve(K,eval(data)).conductor().norm())+' '+str(data)+' '+'\n') newfilewrite.close() 
       
newfile2 = open('/home/bleveque/prelimnewcurvelist.txt') newfile2.readlines() 
        
['N    a-invariants \n', '961 [a+1,-a,0,7*a-23,-24*a+20] \n', '324
[a+1,1,1,-5*a-5,-17*a-13] \n', '225 [1,a-1,0,-a,-71*a-44] \n', '405
[a,-a-1,0,0,-40*a-25] \n', '225 [a,a-1,a+1,-a,3*a-7] \n', '225
[a+1,a,a+1,0,-4*a-3] \n', '605 [a+1,-1,a,-54*a-33,-63*a-39] \n', '605
[a,a+1,0,-6*a-4,-11*a-6] \n', '605 [a+1,a-1,a,7*a-12,-a+2] \n', '605
[1,1,0,-2,7*a+3] \n', '400 [0,-a,0,-53*a-33,-126*a-78] \n', '400
[0,a,0,7*a-13,6*a-12] \n', '400 [0,-a+1,0,-7*a-6,-6*a-6] \n', '81
[a,-a-1,a+1,-73*a-44,-308*a-190] \n', '81
[a,-a-1,a+1,-73*a-44,-308*a-190] \n', '475 [a,a,a+1,39*a+24,63*a+39]
\n', '475 [a+1,a,0,9*a-9,-7*a+15] \n', '475 [1,a-1,a+1,6*a+2,2*a+3] \n',
'891 [1,-1,1,1,43*a+26] \n', '891 [a+1,1,a+1,27*a+17,27*a+17] \n', '775
[1,-a,1,-734*a-454,-11114*a-6869] \n', '775 [a,1,0,-13*a-13,-56*a-8]
\n', '775 [a+1,a+1,0,-104*a-65,-792*a-488] \n', '900
[1,-a-1,1,60*a+37,-855*a-529] \n', '900 [a,-1,1,-8*a+15,45*a-79] \n',
'900 [a+1,-a-1,1,7*a+7,-45*a-34] \n', '361 [0,a+1,a+1,6*a-30,42*a-49]
\n', '361 [0,-a-1,a,-4*a-25,-38*a+19] \n', '475
[a+1,-a+1,1,-15*a-9,-69*a-43] \n', '475 [1,a-1,0,9*a-15,-a+1] \n', '475
[a,a,0,-3,-5*a-3] \n', '475 [a,a-1,a+1,-66*a-40,-92*a-57] \n', '475
[a+1,a+1,1,3*a-3,3*a-7] \n', '475 [1,-a,0,-9*a-6,a] \n', '484
[a+1,-a,1,-61*a-38,-524*a-324] \n', '484 [a,-a+1,1,-9*a-6,-30*a-17] \n',
'484 [a+1,0,1,8*a-15,30*a-47] \n', '484 [1,-a+1,a+1,-5*a-5,23*a+9] \n',
'605 [1,-a,0,-61*a-38,81*a+52] \n', '605 [a+1,a+1,1,-5*a-7,-25*a+21]
\n', '605 [a,a,0,8*a-15,11*a+17] \n', '605
[a+1,-a+1,1,-11*a-9,295*a+181] \n', '725
[0,a,a+1,-223*a-138,-2071*a-1280] \n', '725 [0,-a,a+1,2*a-13,7*a-21]
\n', '725 [0,a-1,a+1,-32*a-21,-116*a-72] \n', '725
[0,a,a,-43*a-28,-203*a-126] \n', '725 [0,-a,a,32*a-53,115*a-187] \n',
'725 [0,a-1,a,-2*a-11,-8*a-13] \n', '775 [0,1,a+1,-30*a-18,8*a+5] \n',
'775 [0,-1,a+1,-5*a+7,3*a-6] \n', '775 [0,-a-1,a+1,-4*a-1,4*a+2] \n',
'775 [0,-a,a,-133*a-83,-820*a-507] \n', '775 [0,a,a,17*a-33,-18*a+19]
\n', '775 [0,-a+1,a,-17*a-16,-45*a-30] \n', '775
[0,-a,a+1,-133*a-83,242*a+149] \n', '775 [0,a,a+1,17*a-33,44*a-75] \n',
'775 [0,-a+1,a+1,-17*a-16,17*a+1] \n', '961 [0,-a,1,-42*a-53,-192*a-140]
\n']
['N    a-invariants \n', '961 [a+1,-a,0,7*a-23,-24*a+20] \n', '324 [a+1,1,1,-5*a-5,-17*a-13] \n', '225 [1,a-1,0,-a,-71*a-44] \n', '405 [a,-a-1,0,0,-40*a-25] \n', '225 [a,a-1,a+1,-a,3*a-7] \n', '225 [a+1,a,a+1,0,-4*a-3] \n', '605 [a+1,-1,a,-54*a-33,-63*a-39] \n', '605 [a,a+1,0,-6*a-4,-11*a-6] \n', '605 [a+1,a-1,a,7*a-12,-a+2] \n', '605 [1,1,0,-2,7*a+3] \n', '400 [0,-a,0,-53*a-33,-126*a-78] \n', '400 [0,a,0,7*a-13,6*a-12] \n', '400 [0,-a+1,0,-7*a-6,-6*a-6] \n', '81 [a,-a-1,a+1,-73*a-44,-308*a-190] \n', '81 [a,-a-1,a+1,-73*a-44,-308*a-190] \n', '475 [a,a,a+1,39*a+24,63*a+39] \n', '475 [a+1,a,0,9*a-9,-7*a+15] \n', '475 [1,a-1,a+1,6*a+2,2*a+3] \n', '891 [1,-1,1,1,43*a+26] \n', '891 [a+1,1,a+1,27*a+17,27*a+17] \n', '775 [1,-a,1,-734*a-454,-11114*a-6869] \n', '775 [a,1,0,-13*a-13,-56*a-8] \n', '775 [a+1,a+1,0,-104*a-65,-792*a-488] \n', '900 [1,-a-1,1,60*a+37,-855*a-529] \n', '900 [a,-1,1,-8*a+15,45*a-79] \n', '900 [a+1,-a-1,1,7*a+7,-45*a-34] \n', '361 [0,a+1,a+1,6*a-30,42*a-49] \n', '361 [0,-a-1,a,-4*a-25,-38*a+19] \n', '475 [a+1,-a+1,1,-15*a-9,-69*a-43] \n', '475 [1,a-1,0,9*a-15,-a+1] \n', '475 [a,a,0,-3,-5*a-3] \n', '475 [a,a-1,a+1,-66*a-40,-92*a-57] \n', '475 [a+1,a+1,1,3*a-3,3*a-7] \n', '475 [1,-a,0,-9*a-6,a] \n', '484 [a+1,-a,1,-61*a-38,-524*a-324] \n', '484 [a,-a+1,1,-9*a-6,-30*a-17] \n', '484 [a+1,0,1,8*a-15,30*a-47] \n', '484 [1,-a+1,a+1,-5*a-5,23*a+9] \n', '605 [1,-a,0,-61*a-38,81*a+52] \n', '605 [a+1,a+1,1,-5*a-7,-25*a+21] \n', '605 [a,a,0,8*a-15,11*a+17] \n', '605 [a+1,-a+1,1,-11*a-9,295*a+181] \n', '725 [0,a,a+1,-223*a-138,-2071*a-1280] \n', '725 [0,-a,a+1,2*a-13,7*a-21] \n', '725 [0,a-1,a+1,-32*a-21,-116*a-72] \n', '725 [0,a,a,-43*a-28,-203*a-126] \n', '725 [0,-a,a,32*a-53,115*a-187] \n', '725 [0,a-1,a,-2*a-11,-8*a-13] \n', '775 [0,1,a+1,-30*a-18,8*a+5] \n', '775 [0,-1,a+1,-5*a+7,3*a-6] \n', '775 [0,-a-1,a+1,-4*a-1,4*a+2] \n', '775 [0,-a,a,-133*a-83,-820*a-507] \n', '775 [0,a,a,17*a-33,-18*a+19] \n', '775 [0,-a+1,a,-17*a-16,-45*a-30] \n', '775 [0,-a,a+1,-133*a-83,242*a+149] \n', '775 [0,a,a+1,17*a-33,44*a-75] \n', '775 [0,-a+1,a+1,-17*a-16,17*a+1] \n', '961 [0,-a,1,-42*a-53,-192*a-140] \n']
PrelimFile = open('/home/bleveque/prelimnewcurvelist.txt') PrelimFile.readline() 
        
'N    a-invariants \n'
'N    a-invariants \n'
new_twist_curves = [] for line in PrelimFile.readlines(): E = EllipticCurve(K,grabber(line)) print 'current curve: ', E.a_invariants() CreLingFile = open('/home/bleveque/cremona_lingham1_curves.txt') omitted_line = CreLingFile.readline() new_ind = 1 for s in CreLingFile.readlines(): F = EllipticCurve(K,grabber(s)) if E.is_isomorphic(F): print 'curve: ', E.a_invariants(), 'is isomorphic to curve: ', F.a_invariants() new_ind = 0 break try: if E.is_isogenous(F): print 'curve: ', E.a_invariants(), 'is isogenous to curve: ', F.a_invariants() break new_ind = 0 except NotImplementedError: print E.a_invariants(), 'seems to be isogenous to ', F.a_invariants(), 'but no isogeny constructed' new_ind = 0 if new_ind: new_twist_curves.append(list(E.a_invariants())) 
        
current curve:  (a + 1, -a, 0, 7*a - 23, -24*a + 20)
current curve:  (a + 1, 1, 1, -5*a - 5, -17*a - 13)
current curve:  (1, a - 1, 0, -a, -71*a - 44)
curve:  (1, a - 1, 0, -a, -71*a - 44) is isogenous to curve:  (a, a, 0,
-1380*a - 853, -30165*a - 18643)
current curve:  (a, -a - 1, 0, 0, -40*a - 25)
current curve:  (a, a - 1, a + 1, -a, 3*a - 7)
curve:  (a, a - 1, a + 1, -a, 3*a - 7) is isogenous to curve:  (a, a, 0,
-1380*a - 853, -30165*a - 18643)
current curve:  (a + 1, a, a + 1, 0, -4*a - 3)
curve:  (a + 1, a, a + 1, 0, -4*a - 3) is isogenous to curve:  (a, a, 0,
-1380*a - 853, -30165*a - 18643)
current curve:  (a + 1, -1, a, -54*a - 33, -63*a - 39)
current curve:  (a, a + 1, 0, -6*a - 4, -11*a - 6)
current curve:  (a + 1, a - 1, a, 7*a - 12, -a + 2)
current curve:  (1, 1, 0, -2, 7*a + 3)
current curve:  (0, -a, 0, -53*a - 33, -126*a - 78)
current curve:  (0, a, 0, 7*a - 13, 6*a - 12)
current curve:  (0, -a + 1, 0, -7*a - 6, -6*a - 6)
current curve:  (a, -a - 1, a + 1, -73*a - 44, -308*a - 190)
current curve:  (a, -a - 1, a + 1, -73*a - 44, -308*a - 190)
current curve:  (a, a, a + 1, 39*a + 24, 63*a + 39)
current curve:  (a + 1, a, 0, 9*a - 9, -7*a + 15)
current curve:  (1, a - 1, a + 1, 6*a + 2, 2*a + 3)
current curve:  (1, -1, 1, 1, 43*a + 26)
current curve:  (a + 1, 1, a + 1, 27*a + 17, 27*a + 17)
current curve:  (1, -a, 1, -734*a - 454, -11114*a - 6869)
current curve:  (a, 1, 0, -13*a - 13, -56*a - 8)
current curve:  (a + 1, a + 1, 0, -104*a - 65, -792*a - 488)
current curve:  (1, -a - 1, 1, 60*a + 37, -855*a - 529)
curve:  (1, -a - 1, 1, 60*a + 37, -855*a - 529) is isogenous to curve: 
(1, -a - 1, 1, -740*a - 463, -9975*a - 6169)
current curve:  (a, -1, 1, -8*a + 15, 45*a - 79)
curve:  (a, -1, 1, -8*a + 15, 45*a - 79) is isogenous to curve:  (1, -a
- 1, 1, -740*a - 463, -9975*a - 6169)
current curve:  (a + 1, -a - 1, 1, 7*a + 7, -45*a - 34)
curve:  (a + 1, -a - 1, 1, 7*a + 7, -45*a - 34) is isogenous to curve: 
(1, -a - 1, 1, -740*a - 463, -9975*a - 6169)
current curve:  (0, a + 1, a + 1, 6*a - 30, 42*a - 49)
curve:  (0, a + 1, a + 1, 6*a - 30, 42*a - 49) is isomorphic to curve: 
(0, -1, a + 1, -67*a - 46, 342*a + 209)
current curve:  (0, -a - 1, a, -4*a - 25, -38*a + 19)
current curve:  (a + 1, -a + 1, 1, -15*a - 9, -69*a - 43)
current curve:  (1, a - 1, 0, 9*a - 15, -a + 1)
current curve:  (a, a, 0, -3, -5*a - 3)
current curve:  (a, a - 1, a + 1, -66*a - 40, -92*a - 57)
curve:  (a, a - 1, a + 1, -66*a - 40, -92*a - 57) is isogenous to curve:
(1, -a, 0, -109*a - 81, -649*a - 425)
current curve:  (a + 1, a + 1, 1, 3*a - 3, 3*a - 7)
curve:  (a + 1, a + 1, 1, 3*a - 3, 3*a - 7) is isogenous to curve:  (1,
-a, 0, -109*a - 81, -649*a - 425)
current curve:  (1, -a, 0, -9*a - 6, a)
curve:  (1, -a, 0, -9*a - 6, a) is isogenous to curve:  (1, -a, 0,
-109*a - 81, -649*a - 425)
current curve:  (a + 1, -a, 1, -61*a - 38, -524*a - 324)
current curve:  (a, -a + 1, 1, -9*a - 6, -30*a - 17)
current curve:  (a + 1, 0, 1, 8*a - 15, 30*a - 47)
curve:  (a + 1, 0, 1, 8*a - 15, 30*a - 47) is isomorphic to curve:  (1,
-a + 1, a + 1, -5*a - 5, 23*a + 9)
current curve:  (1, -a + 1, a + 1, -5*a - 5, 23*a + 9)
curve:  (1, -a + 1, a + 1, -5*a - 5, 23*a + 9) is isomorphic to curve: 
(1, -a + 1, a + 1, -5*a - 5, 23*a + 9)
current curve:  (1, -a, 0, -61*a - 38, 81*a + 52)
current curve:  (a + 1, a + 1, 1, -5*a - 7, -25*a + 21)
current curve:  (a, a, 0, 8*a - 15, 11*a + 17)
curve:  (a, a, 0, 8*a - 15, 11*a + 17) is isomorphic to curve:  (a + 1,
a, a + 1, 421*a - 681, -1049*a + 1697)
current curve:  (a + 1, -a + 1, 1, -11*a - 9, 295*a + 181)
curve:  (a + 1, -a + 1, 1, -11*a - 9, 295*a + 181) is isomorphic to
curve:  (a + 1, a, a + 1, 421*a - 681, -1049*a + 1697)
current curve:  (0, a, a + 1, -223*a - 138, -2071*a - 1280)
current curve:  (0, -a, a + 1, 2*a - 13, 7*a - 21)
current curve:  (0, a - 1, a + 1, -32*a - 21, -116*a - 72)
current curve:  (0, a, a, -43*a - 28, -203*a - 126)
current curve:  (0, -a, a, 32*a - 53, 115*a - 187)
current curve:  (0, a - 1, a, -2*a - 11, -8*a - 13)
current curve:  (0, 1, a + 1, -30*a - 18, 8*a + 5)
current curve:  (0, -1, a + 1, -5*a + 7, 3*a - 6)
current curve:  (0, -a - 1, a + 1, -4*a - 1, 4*a + 2)
current curve:  (0, -a, a, -133*a - 83, -820*a - 507)
current curve:  (0, a, a, 17*a - 33, -18*a + 19)
current curve:  (0, -a + 1, a, -17*a - 16, -45*a - 30)
current curve:  (0, -a, a + 1, -133*a - 83, 242*a + 149)
current curve:  (0, a, a + 1, 17*a - 33, 44*a - 75)
current curve:  (0, -a + 1, a + 1, -17*a - 16, 17*a + 1)
current curve:  (0, -a, 1, -42*a - 53, -192*a - 140)
current curve:  (a + 1, -a, 0, 7*a - 23, -24*a + 20)
current curve:  (a + 1, 1, 1, -5*a - 5, -17*a - 13)
current curve:  (1, a - 1, 0, -a, -71*a - 44)
curve:  (1, a - 1, 0, -a, -71*a - 44) is isogenous to curve:  (a, a, 0, -1380*a - 853, -30165*a - 18643)
current curve:  (a, -a - 1, 0, 0, -40*a - 25)
current curve:  (a, a - 1, a + 1, -a, 3*a - 7)
curve:  (a, a - 1, a + 1, -a, 3*a - 7) is isogenous to curve:  (a, a, 0, -1380*a - 853, -30165*a - 18643)
current curve:  (a + 1, a, a + 1, 0, -4*a - 3)
curve:  (a + 1, a, a + 1, 0, -4*a - 3) is isogenous to curve:  (a, a, 0, -1380*a - 853, -30165*a - 18643)
current curve:  (a + 1, -1, a, -54*a - 33, -63*a - 39)
current curve:  (a, a + 1, 0, -6*a - 4, -11*a - 6)
current curve:  (a + 1, a - 1, a, 7*a - 12, -a + 2)
current curve:  (1, 1, 0, -2, 7*a + 3)
current curve:  (0, -a, 0, -53*a - 33, -126*a - 78)
current curve:  (0, a, 0, 7*a - 13, 6*a - 12)
current curve:  (0, -a + 1, 0, -7*a - 6, -6*a - 6)
current curve:  (a, -a - 1, a + 1, -73*a - 44, -308*a - 190)
current curve:  (a, -a - 1, a + 1, -73*a - 44, -308*a - 190)
current curve:  (a, a, a + 1, 39*a + 24, 63*a + 39)
current curve:  (a + 1, a, 0, 9*a - 9, -7*a + 15)
current curve:  (1, a - 1, a + 1, 6*a + 2, 2*a + 3)
current curve:  (1, -1, 1, 1, 43*a + 26)
current curve:  (a + 1, 1, a + 1, 27*a + 17, 27*a + 17)
current curve:  (1, -a, 1, -734*a - 454, -11114*a - 6869)
current curve:  (a, 1, 0, -13*a - 13, -56*a - 8)
current curve:  (a + 1, a + 1, 0, -104*a - 65, -792*a - 488)
current curve:  (1, -a - 1, 1, 60*a + 37, -855*a - 529)
curve:  (1, -a - 1, 1, 60*a + 37, -855*a - 529) is isogenous to curve:  (1, -a - 1, 1, -740*a - 463, -9975*a - 6169)
current curve:  (a, -1, 1, -8*a + 15, 45*a - 79)
curve:  (a, -1, 1, -8*a + 15, 45*a - 79) is isogenous to curve:  (1, -a - 1, 1, -740*a - 463, -9975*a - 6169)
current curve:  (a + 1, -a - 1, 1, 7*a + 7, -45*a - 34)
curve:  (a + 1, -a - 1, 1, 7*a + 7, -45*a - 34) is isogenous to curve:  (1, -a - 1, 1, -740*a - 463, -9975*a - 6169)
current curve:  (0, a + 1, a + 1, 6*a - 30, 42*a - 49)
curve:  (0, a + 1, a + 1, 6*a - 30, 42*a - 49) is isomorphic to curve:  (0, -1, a + 1, -67*a - 46, 342*a + 209)
current curve:  (0, -a - 1, a, -4*a - 25, -38*a + 19)
current curve:  (a + 1, -a + 1, 1, -15*a - 9, -69*a - 43)
current curve:  (1, a - 1, 0, 9*a - 15, -a + 1)
current curve:  (a, a, 0, -3, -5*a - 3)
current curve:  (a, a - 1, a + 1, -66*a - 40, -92*a - 57)
curve:  (a, a - 1, a + 1, -66*a - 40, -92*a - 57) is isogenous to curve:  (1, -a, 0, -109*a - 81, -649*a - 425)
current curve:  (a + 1, a + 1, 1, 3*a - 3, 3*a - 7)
curve:  (a + 1, a + 1, 1, 3*a - 3, 3*a - 7) is isogenous to curve:  (1, -a, 0, -109*a - 81, -649*a - 425)
current curve:  (1, -a, 0, -9*a - 6, a)
curve:  (1, -a, 0, -9*a - 6, a) is isogenous to curve:  (1, -a, 0, -109*a - 81, -649*a - 425)
current curve:  (a + 1, -a, 1, -61*a - 38, -524*a - 324)
current curve:  (a, -a + 1, 1, -9*a - 6, -30*a - 17)
current curve:  (a + 1, 0, 1, 8*a - 15, 30*a - 47)
curve:  (a + 1, 0, 1, 8*a - 15, 30*a - 47) is isomorphic to curve:  (1, -a + 1, a + 1, -5*a - 5, 23*a + 9)
current curve:  (1, -a + 1, a + 1, -5*a - 5, 23*a + 9)
curve:  (1, -a + 1, a + 1, -5*a - 5, 23*a + 9) is isomorphic to curve:  (1, -a + 1, a + 1, -5*a - 5, 23*a + 9)
current curve:  (1, -a, 0, -61*a - 38, 81*a + 52)
current curve:  (a + 1, a + 1, 1, -5*a - 7, -25*a + 21)
current curve:  (a, a, 0, 8*a - 15, 11*a + 17)
curve:  (a, a, 0, 8*a - 15, 11*a + 17) is isomorphic to curve:  (a + 1, a, a + 1, 421*a - 681, -1049*a + 1697)
current curve:  (a + 1, -a + 1, 1, -11*a - 9, 295*a + 181)
curve:  (a + 1, -a + 1, 1, -11*a - 9, 295*a + 181) is isomorphic to curve:  (a + 1, a, a + 1, 421*a - 681, -1049*a + 1697)
current curve:  (0, a, a + 1, -223*a - 138, -2071*a - 1280)
current curve:  (0, -a, a + 1, 2*a - 13, 7*a - 21)
current curve:  (0, a - 1, a + 1, -32*a - 21, -116*a - 72)
current curve:  (0, a, a, -43*a - 28, -203*a - 126)
current curve:  (0, -a, a, 32*a - 53, 115*a - 187)
current curve:  (0, a - 1, a, -2*a - 11, -8*a - 13)
current curve:  (0, 1, a + 1, -30*a - 18, 8*a + 5)
current curve:  (0, -1, a + 1, -5*a + 7, 3*a - 6)
current curve:  (0, -a - 1, a + 1, -4*a - 1, 4*a + 2)
current curve:  (0, -a, a, -133*a - 83, -820*a - 507)
current curve:  (0, a, a, 17*a - 33, -18*a + 19)
current curve:  (0, -a + 1, a, -17*a - 16, -45*a - 30)
current curve:  (0, -a, a + 1, -133*a - 83, 242*a + 149)
current curve:  (0, a, a + 1, 17*a - 33, 44*a - 75)
current curve:  (0, -a + 1, a + 1, -17*a - 16, 17*a + 1)
current curve:  (0, -a, 1, -42*a - 53, -192*a - 140)
##### # Now we put the purely new curves in a file ##### twistfile = open('/home/bleveque/new_curves_via_twist_1.txt','w') twistfile.write('New Curves Found Via Quadratic Twist \n') twistfile.write('==================================== \n') twistfile.write('N a-invariants \n') for curve in new_twist_curves: twistfile.write(str(EllipticCurve(K,curve).conductor().norm())+' '+str(curve).replace(' ','')+' '+'\n') twistfile.close() 
       
######## # Print out new curves! ######## twistfile2 = open('/home/bleveque/new_curves_via_twist_1.txt') for line in twistfile2.readlines(): print line[:-1] 
        
New Curves Found Via Quadratic Twist 
==================================== 
N       a-invariants 
961 [a+1,-a,0,7*a-23,-24*a+20] 
324 [a+1,1,1,-5*a-5,-17*a-13] 
225 [1,a-1,0,-a,-71*a-44] 
405 [a,-a-1,0,0,-40*a-25] 
225 [a,a-1,a+1,-a,3*a-7] 
225 [a+1,a,a+1,0,-4*a-3] 
605 [a+1,-1,a,-54*a-33,-63*a-39] 
605 [a,a+1,0,-6*a-4,-11*a-6] 
605 [a+1,a-1,a,7*a-12,-a+2] 
605 [1,1,0,-2,7*a+3] 
400 [0,-a,0,-53*a-33,-126*a-78] 
400 [0,a,0,7*a-13,6*a-12] 
400 [0,-a+1,0,-7*a-6,-6*a-6] 
81 [a,-a-1,a+1,-73*a-44,-308*a-190] 
81 [a,-a-1,a+1,-73*a-44,-308*a-190] 
475 [a,a,a+1,39*a+24,63*a+39] 
475 [a+1,a,0,9*a-9,-7*a+15] 
475 [1,a-1,a+1,6*a+2,2*a+3] 
891 [1,-1,1,1,43*a+26] 
891 [a+1,1,a+1,27*a+17,27*a+17] 
775 [1,-a,1,-734*a-454,-11114*a-6869] 
775 [a,1,0,-13*a-13,-56*a-8] 
775 [a+1,a+1,0,-104*a-65,-792*a-488] 
900 [1,-a-1,1,60*a+37,-855*a-529] 
900 [a,-1,1,-8*a+15,45*a-79] 
900 [a+1,-a-1,1,7*a+7,-45*a-34] 
361 [0,-a-1,a,-4*a-25,-38*a+19] 
475 [a+1,-a+1,1,-15*a-9,-69*a-43] 
475 [1,a-1,0,9*a-15,-a+1] 
475 [a,a,0,-3,-5*a-3] 
475 [a,a-1,a+1,-66*a-40,-92*a-57] 
475 [a+1,a+1,1,3*a-3,3*a-7] 
475 [1,-a,0,-9*a-6,a] 
484 [a+1,-a,1,-61*a-38,-524*a-324] 
484 [a,-a+1,1,-9*a-6,-30*a-17] 
605 [1,-a,0,-61*a-38,81*a+52] 
605 [a+1,a+1,1,-5*a-7,-25*a+21] 
725 [0,a,a+1,-223*a-138,-2071*a-1280] 
725 [0,-a,a+1,2*a-13,7*a-21] 
725 [0,a-1,a+1,-32*a-21,-116*a-72] 
725 [0,a,a,-43*a-28,-203*a-126] 
725 [0,-a,a,32*a-53,115*a-187] 
725 [0,a-1,a,-2*a-11,-8*a-13] 
775 [0,1,a+1,-30*a-18,8*a+5] 
775 [0,-1,a+1,-5*a+7,3*a-6] 
775 [0,-a-1,a+1,-4*a-1,4*a+2] 
775 [0,-a,a,-133*a-83,-820*a-507] 
775 [0,a,a,17*a-33,-18*a+19] 
775 [0,-a+1,a,-17*a-16,-45*a-30] 
775 [0,-a,a+1,-133*a-83,242*a+149] 
775 [0,a,a+1,17*a-33,44*a-75] 
775 [0,-a+1,a+1,-17*a-16,17*a+1] 
961 [0,-a,1,-42*a-53,-192*a-140] 
New Curves Found Via Quadratic Twist 
==================================== 
N       a-invariants 
961 [a+1,-a,0,7*a-23,-24*a+20] 
324 [a+1,1,1,-5*a-5,-17*a-13] 
225 [1,a-1,0,-a,-71*a-44] 
405 [a,-a-1,0,0,-40*a-25] 
225 [a,a-1,a+1,-a,3*a-7] 
225 [a+1,a,a+1,0,-4*a-3] 
605 [a+1,-1,a,-54*a-33,-63*a-39] 
605 [a,a+1,0,-6*a-4,-11*a-6] 
605 [a+1,a-1,a,7*a-12,-a+2] 
605 [1,1,0,-2,7*a+3] 
400 [0,-a,0,-53*a-33,-126*a-78] 
400 [0,a,0,7*a-13,6*a-12] 
400 [0,-a+1,0,-7*a-6,-6*a-6] 
81 [a,-a-1,a+1,-73*a-44,-308*a-190] 
81 [a,-a-1,a+1,-73*a-44,-308*a-190] 
475 [a,a,a+1,39*a+24,63*a+39] 
475 [a+1,a,0,9*a-9,-7*a+15] 
475 [1,a-1,a+1,6*a+2,2*a+3] 
891 [1,-1,1,1,43*a+26] 
891 [a+1,1,a+1,27*a+17,27*a+17] 
775 [1,-a,1,-734*a-454,-11114*a-6869] 
775 [a,1,0,-13*a-13,-56*a-8] 
775 [a+1,a+1,0,-104*a-65,-792*a-488] 
900 [1,-a-1,1,60*a+37,-855*a-529] 
900 [a,-1,1,-8*a+15,45*a-79] 
900 [a+1,-a-1,1,7*a+7,-45*a-34] 
361 [0,-a-1,a,-4*a-25,-38*a+19] 
475 [a+1,-a+1,1,-15*a-9,-69*a-43] 
475 [1,a-1,0,9*a-15,-a+1] 
475 [a,a,0,-3,-5*a-3] 
475 [a,a-1,a+1,-66*a-40,-92*a-57] 
475 [a+1,a+1,1,3*a-3,3*a-7] 
475 [1,-a,0,-9*a-6,a] 
484 [a+1,-a,1,-61*a-38,-524*a-324] 
484 [a,-a+1,1,-9*a-6,-30*a-17] 
605 [1,-a,0,-61*a-38,81*a+52] 
605 [a+1,a+1,1,-5*a-7,-25*a+21] 
725 [0,a,a+1,-223*a-138,-2071*a-1280] 
725 [0,-a,a+1,2*a-13,7*a-21] 
725 [0,a-1,a+1,-32*a-21,-116*a-72] 
725 [0,a,a,-43*a-28,-203*a-126] 
725 [0,-a,a,32*a-53,115*a-187] 
725 [0,a-1,a,-2*a-11,-8*a-13] 
775 [0,1,a+1,-30*a-18,8*a+5] 
775 [0,-1,a+1,-5*a+7,3*a-6] 
775 [0,-a-1,a+1,-4*a-1,4*a+2] 
775 [0,-a,a,-133*a-83,-820*a-507] 
775 [0,a,a,17*a-33,-18*a+19] 
775 [0,-a+1,a,-17*a-16,-45*a-30] 
775 [0,-a,a+1,-133*a-83,242*a+149] 
775 [0,a,a+1,17*a-33,44*a-75] 
775 [0,-a+1,a+1,-17*a-16,17*a+1] 
961 [0,-a,1,-42*a-53,-192*a-140]
twistfile2 = open('/home/bleveque/new_curves_via_twist_1.txt') twistfile2copy = open('/home/bleveque/new_curves_via_twist_1_copy.txt','w') for line in twistfile2.readlines(): twistfile2copy.write(line) twistfile2.close() twistfile2copy.close() 
       
twf2c2 = open('/home/bleveque/new_curves_via_twist_1_copy.txt') for i in twf2c2.readlines(): print i 
        
New Curves Found Via Quadratic Twist 

==================================== 

N       a-invariants 

961 [a+1,-a,0,7*a-23,-24*a+20] 

324 [a+1,1,1,-5*a-5,-17*a-13] 

225 [1,a-1,0,-a,-71*a-44] 

405 [a,-a-1,0,0,-40*a-25] 

225 [a,a-1,a+1,-a,3*a-7] 

225 [a+1,a,a+1,0,-4*a-3] 

605 [a+1,-1,a,-54*a-33,-63*a-39] 

605 [a,a+1,0,-6*a-4,-11*a-6] 

605 [a+1,a-1,a,7*a-12,-a+2] 

605 [1,1,0,-2,7*a+3] 

400 [0,-a,0,-53*a-33,-126*a-78] 

400 [0,a,0,7*a-13,6*a-12] 

400 [0,-a+1,0,-7*a-6,-6*a-6] 

81 [a,-a-1,a+1,-73*a-44,-308*a-190] 

81 [a,-a-1,a+1,-73*a-44,-308*a-190] 

475 [a,a,a+1,39*a+24,63*a+39] 

475 [a+1,a,0,9*a-9,-7*a+15] 

475 [1,a-1,a+1,6*a+2,2*a+3] 

891 [1,-1,1,1,43*a+26] 

891 [a+1,1,a+1,27*a+17,27*a+17] 

775 [1,-a,1,-734*a-454,-11114*a-6869] 

775 [a,1,0,-13*a-13,-56*a-8] 

775 [a+1,a+1,0,-104*a-65,-792*a-488] 

900 [1,-a-1,1,60*a+37,-855*a-529] 

900 [a,-1,1,-8*a+15,45*a-79] 

900 [a+1,-a-1,1,7*a+7,-45*a-34] 

361 [0,-a-1,a,-4*a-25,-38*a+19] 

475 [a+1,-a+1,1,-15*a-9,-69*a-43] 

475 [1,a-1,0,9*a-15,-a+1] 

475 [a,a,0,-3,-5*a-3] 

475 [a,a-1,a+1,-66*a-40,-92*a-57] 

475 [a+1,a+1,1,3*a-3,3*a-7] 

475 [1,-a,0,-9*a-6,a] 

484 [a+1,-a,1,-61*a-38,-524*a-324] 

484 [a,-a+1,1,-9*a-6,-30*a-17] 

605 [1,-a,0,-61*a-38,81*a+52] 

605 [a+1,a+1,1,-5*a-7,-25*a+21] 

725 [0,a,a+1,-223*a-138,-2071*a-1280] 

725 [0,-a,a+1,2*a-13,7*a-21] 

725 [0,a-1,a+1,-32*a-21,-116*a-72] 

725 [0,a,a,-43*a-28,-203*a-126] 

725 [0,-a,a,32*a-53,115*a-187] 

725 [0,a-1,a,-2*a-11,-8*a-13] 

775 [0,1,a+1,-30*a-18,8*a+5] 

775 [0,-1,a+1,-5*a+7,3*a-6] 

775 [0,-a-1,a+1,-4*a-1,4*a+2] 

775 [0,-a,a,-133*a-83,-820*a-507] 

775 [0,a,a,17*a-33,-18*a+19] 

775 [0,-a+1,a,-17*a-16,-45*a-30] 

775 [0,-a,a+1,-133*a-83,242*a+149] 

775 [0,a,a+1,17*a-33,44*a-75] 

775 [0,-a+1,a+1,-17*a-16,17*a+1] 

961 [0,-a,1,-42*a-53,-192*a-140] 
New Curves Found Via Quadratic Twist 

==================================== 

N       a-invariants 

961 [a+1,-a,0,7*a-23,-24*a+20] 

324 [a+1,1,1,-5*a-5,-17*a-13] 

225 [1,a-1,0,-a,-71*a-44] 

405 [a,-a-1,0,0,-40*a-25] 

225 [a,a-1,a+1,-a,3*a-7] 

225 [a+1,a,a+1,0,-4*a-3] 

605 [a+1,-1,a,-54*a-33,-63*a-39] 

605 [a,a+1,0,-6*a-4,-11*a-6] 

605 [a+1,a-1,a,7*a-12,-a+2] 

605 [1,1,0,-2,7*a+3] 

400 [0,-a,0,-53*a-33,-126*a-78] 

400 [0,a,0,7*a-13,6*a-12] 

400 [0,-a+1,0,-7*a-6,-6*a-6] 

81 [a,-a-1,a+1,-73*a-44,-308*a-190] 

81 [a,-a-1,a+1,-73*a-44,-308*a-190] 

475 [a,a,a+1,39*a+24,63*a+39] 

475 [a+1,a,0,9*a-9,-7*a+15] 

475 [1,a-1,a+1,6*a+2,2*a+3] 

891 [1,-1,1,1,43*a+26] 

891 [a+1,1,a+1,27*a+17,27*a+17] 

775 [1,-a,1,-734*a-454,-11114*a-6869] 

775 [a,1,0,-13*a-13,-56*a-8] 

775 [a+1,a+1,0,-104*a-65,-792*a-488] 

900 [1,-a-1,1,60*a+37,-855*a-529] 

900 [a,-1,1,-8*a+15,45*a-79] 

900 [a+1,-a-1,1,7*a+7,-45*a-34] 

361 [0,-a-1,a,-4*a-25,-38*a+19] 

475 [a+1,-a+1,1,-15*a-9,-69*a-43] 

475 [1,a-1,0,9*a-15,-a+1] 

475 [a,a,0,-3,-5*a-3] 

475 [a,a-1,a+1,-66*a-40,-92*a-57] 

475 [a+1,a+1,1,3*a-3,3*a-7] 

475 [1,-a,0,-9*a-6,a] 

484 [a+1,-a,1,-61*a-38,-524*a-324] 

484 [a,-a+1,1,-9*a-6,-30*a-17] 

605 [1,-a,0,-61*a-38,81*a+52] 

605 [a+1,a+1,1,-5*a-7,-25*a+21] 

725 [0,a,a+1,-223*a-138,-2071*a-1280] 

725 [0,-a,a+1,2*a-13,7*a-21] 

725 [0,a-1,a+1,-32*a-21,-116*a-72] 

725 [0,a,a,-43*a-28,-203*a-126] 

725 [0,-a,a,32*a-53,115*a-187] 

725 [0,a-1,a,-2*a-11,-8*a-13] 

775 [0,1,a+1,-30*a-18,8*a+5] 

775 [0,-1,a+1,-5*a+7,3*a-6] 

775 [0,-a-1,a+1,-4*a-1,4*a+2] 

775 [0,-a,a,-133*a-83,-820*a-507] 

775 [0,a,a,17*a-33,-18*a+19] 

775 [0,-a+1,a,-17*a-16,-45*a-30] 

775 [0,-a,a+1,-133*a-83,242*a+149] 

775 [0,a,a+1,17*a-33,44*a-75] 

775 [0,-a+1,a+1,-17*a-16,17*a+1] 

961 [0,-a,1,-42*a-53,-192*a-140]
tf2 = open('/home/bleveque/new_curves_via_twist_1.txt') discard = tf2.readline() discard = tf2.readline() discard = tf2.readline() final_curve_list = [] for line in tf2.readlines(): final_curve_list.append(grabber(line)) tf22 = open('/home/bleveque/new_curves_via_twist_1.txt') discard = tf22.readline() discard = tf22.readline() discard = tf22.readline() for line in tf22.readlines(): E = EllipticCurve(K,grabber(line)) print 'current curve: ',list(E.a_invariants()) tf2c = open('/home/bleveque/new_curves_via_twist_1_copy.txt') discard = tf2c.readline() discard = tf2c.readline() discard = tf2c.readline() for s in tf2c.readlines(): F = EllipticCurve(K,grabber(s)) if E.a_invariants() != F.a_invariants(): if E.is_isomorphic(F): if list(F.a_invariants final_curve_list.remove(list(F.a_invariants())) print 'curve: ',list(E.a_invariants()),' is isomorphic to curve: ',list(F.a_invariants()) break try: if E.is_isogenous(F): final_curve_list.remove(list(F.a_invariants())) print 'curve: ',list(E.a_invariants()),' is isogenous to curve: ',list(F.a_invariants()) break except NotImplementedError: final_curve_list.remove(list(F.a_invariants())) print E.a_invariants(), 'seems to be isog. to ', F.a_invariants(), 'but no isogeny constructed' print final_curve_list 
        
current curve:  [a + 1, -a, 0, 7*a - 23, -24*a + 20]
current curve:  [a + 1, 1, 1, -5*a - 5, -17*a - 13]
current curve:  [1, a - 1, 0, -a, -71*a - 44]
curve:  [1, a - 1, 0, -a, -71*a - 44]  is isomorphic to curve:  [a, a -
1, a + 1, -a, 3*a - 7]
current curve:  [a, -a - 1, 0, 0, -40*a - 25]
current curve:  [a, a - 1, a + 1, -a, 3*a - 7]
curve:  [a, a - 1, a + 1, -a, 3*a - 7]  is isomorphic to curve:  [1, a -
1, 0, -a, -71*a - 44]
current curve:  [a + 1, a, a + 1, 0, -4*a - 3]
Traceback (click to the left of this block for traceback)
...
ValueError: list.remove(x): x not in list
current curve:  [a + 1, -a, 0, 7*a - 23, -24*a + 20]
current curve:  [a + 1, 1, 1, -5*a - 5, -17*a - 13]
current curve:  [1, a - 1, 0, -a, -71*a - 44]
curve:  [1, a - 1, 0, -a, -71*a - 44]  is isomorphic to curve:  [a, a - 1, a + 1, -a, 3*a - 7]
current curve:  [a, -a - 1, 0, 0, -40*a - 25]
current curve:  [a, a - 1, a + 1, -a, 3*a - 7]
curve:  [a, a - 1, a + 1, -a, 3*a - 7]  is isomorphic to curve:  [1, a - 1, 0, -a, -71*a - 44]
current curve:  [a + 1, a, a + 1, 0, -4*a - 3]
Traceback (most recent call last):    final_curve_list = []
  File "", line 1, in <module>
    
  File "/tmp/tmpnTLVHC/___code___.py", line 29, in <module>
    final_curve_list.remove(list(F.a_invariants()))
ValueError: list.remove(x): x not in list
tf2 = open('/home/bleveque/new_curves_via_twist_1.txt') discard = tf2.readline() discard = tf2.readline() discard = tf2.readline() final_curve_list = [] for line in tf2.readlines(): final_curve_list.append(grabber(line)) 
       
for curr_data in final_curve_list: E = EllipticCurve(K,curr_data) print 'current curve: ',list(E.a_invariants()) for sec_data in final_curve_list: F = EllipticCurve(K,sec_data) if E.a_invariants() != F.a_invariants(): if E.is_isomorphic(F): final_curve_list.remove(list(F.a_invariants())) print 'curve: ',list(E.a_invariants()),' is isomorphic to curve: ',list(F.a_invariants()) break try: if E.is_isogenous(F): final_curve_list.remove(list(F.a_invariants())) print 'curve: ',list(E.a_invariants()),' is isogenous to curve: ',list(F.a_invariants()) break except NotImplementedError: final_curve_list.remove(list(F.a_invariants())) print E.a_invariants(), 'seems to be isog. to ', F.a_invariants(), 'but no isogeny constructed' print final_curve_list 
        
current curve:  [a + 1, -a, 0, 7*a - 23, -24*a + 20]
current curve:  [a + 1, 1, 1, -5*a - 5, -17*a - 13]
current curve:  [1, a - 1, 0, -a, -71*a - 44]
curve:  [1, a - 1, 0, -a, -71*a - 44]  is isomorphic to curve:  [a, a -
1, a + 1, -a, 3*a - 7]
current curve:  [a, -a - 1, 0, 0, -40*a - 25]
current curve:  [a + 1, a, a + 1, 0, -4*a - 3]
curve:  [a + 1, a, a + 1, 0, -4*a - 3]  is isomorphic to curve:  [1, a -
1, 0, -a, -71*a - 44]
current curve:  [a, a + 1, 0, -6*a - 4, -11*a - 6]
curve:  [a, a + 1, 0, -6*a - 4, -11*a - 6]  is isomorphic to curve:  [a
+ 1, -1, a, -54*a - 33, -63*a - 39]
current curve:  [1, 1, 0, -2, 7*a + 3]
curve:  [1, 1, 0, -2, 7*a + 3]  is isomorphic to curve:  [a + 1, a - 1,
a, 7*a - 12, -a + 2]
current curve:  [0, a, 0, 7*a - 13, 6*a - 12]
curve:  [0, a, 0, 7*a - 13, 6*a - 12]  is isomorphic to curve:  [0, -a,
0, -53*a - 33, -126*a - 78]
current curve:  [a, -a - 1, a + 1, -73*a - 44, -308*a - 190]
current curve:  [a, -a - 1, a + 1, -73*a - 44, -308*a - 190]
current curve:  [a, a, a + 1, 39*a + 24, 63*a + 39]
curve:  [a, a, a + 1, 39*a + 24, 63*a + 39]  is isomorphic to curve:  [a
+ 1, a, 0, 9*a - 9, -7*a + 15]
current curve:  [1, a - 1, a + 1, 6*a + 2, 2*a + 3]
curve:  [1, a - 1, a + 1, 6*a + 2, 2*a + 3]  is isomorphic to curve: 
[a, a, a + 1, 39*a + 24, 63*a + 39]
current curve:  [a + 1, 1, a + 1, 27*a + 17, 27*a + 17]
current curve:  [1, -a, 1, -734*a - 454, -11114*a - 6869]
curve:  [1, -a, 1, -734*a - 454, -11114*a - 6869]  is isomorphic to
curve:  [a, 1, 0, -13*a - 13, -56*a - 8]
current curve:  [a + 1, a + 1, 0, -104*a - 65, -792*a - 488]
curve:  [a + 1, a + 1, 0, -104*a - 65, -792*a - 488]  is isomorphic to
curve:  [1, -a, 1, -734*a - 454, -11114*a - 6869]
current curve:  [a, -1, 1, -8*a + 15, 45*a - 79]
curve:  [a, -1, 1, -8*a + 15, 45*a - 79]  is isomorphic to curve:  [1,
-a - 1, 1, 60*a + 37, -855*a - 529]
current curve:  [0, -a - 1, a, -4*a - 25, -38*a + 19]
current curve:  [a + 1, -a + 1, 1, -15*a - 9, -69*a - 43]
curve:  [a + 1, -a + 1, 1, -15*a - 9, -69*a - 43]  is isomorphic to
curve:  [1, a - 1, 0, 9*a - 15, -a + 1]
current curve:  [a, a, 0, -3, -5*a - 3]
curve:  [a, a, 0, -3, -5*a - 3]  is isomorphic to curve:  [a + 1, -a +
1, 1, -15*a - 9, -69*a - 43]
current curve:  [a + 1, a + 1, 1, 3*a - 3, 3*a - 7]
curve:  [a + 1, a + 1, 1, 3*a - 3, 3*a - 7]  is isomorphic to curve: 
[a, a - 1, a + 1, -66*a - 40, -92*a - 57]
current curve:  [a + 1, -a, 1, -61*a - 38, -524*a - 324]
curve:  [a + 1, -a, 1, -61*a - 38, -524*a - 324]  is isomorphic to
curve:  [a, -a + 1, 1, -9*a - 6, -30*a - 17]
current curve:  [1, -a, 0, -61*a - 38, 81*a + 52]
curve:  [1, -a, 0, -61*a - 38, 81*a + 52]  is isomorphic to curve:  [a +
1, a + 1, 1, -5*a - 7, -25*a + 21]
current curve:  [0, a, a + 1, -223*a - 138, -2071*a - 1280]
curve:  [0, a, a + 1, -223*a - 138, -2071*a - 1280]  is isomorphic to
curve:  [0, -a, a + 1, 2*a - 13, 7*a - 21]
current curve:  [0, a - 1, a + 1, -32*a - 21, -116*a - 72]
curve:  [0, a - 1, a + 1, -32*a - 21, -116*a - 72]  is isomorphic to
curve:  [0, a, a + 1, -223*a - 138, -2071*a - 1280]
current curve:  [0, -a, a, 32*a - 53, 115*a - 187]
curve:  [0, -a, a, 32*a - 53, 115*a - 187]  is isomorphic to curve:  [0,
a, a, -43*a - 28, -203*a - 126]
current curve:  [0, 1, a + 1, -30*a - 18, 8*a + 5]
curve:  [0, 1, a + 1, -30*a - 18, 8*a + 5]  is isomorphic to curve:  [0,
-1, a + 1, -5*a + 7, 3*a - 6]
current curve:  [0, -a - 1, a + 1, -4*a - 1, 4*a + 2]
curve:  [0, -a - 1, a + 1, -4*a - 1, 4*a + 2]  is isomorphic to curve: 
[0, 1, a + 1, -30*a - 18, 8*a + 5]
current curve:  [0, a, a, 17*a - 33, -18*a + 19]
curve:  [0, a, a, 17*a - 33, -18*a + 19]  is isomorphic to curve:  [0,
-a, a, -133*a - 83, -820*a - 507]
current curve:  [0, -a, a + 1, -133*a - 83, 242*a + 149]
curve:  [0, -a, a + 1, -133*a - 83, 242*a + 149]  is isomorphic to
curve:  [0, a, a + 1, 17*a - 33, 44*a - 75]
current curve:  [0, -a + 1, a + 1, -17*a - 16, 17*a + 1]
curve:  [0, -a + 1, a + 1, -17*a - 16, 17*a + 1]  is isomorphic to
curve:  [0, -a, a + 1, -133*a - 83, 242*a + 149]
[[a + 1, -a, 0, 7*a - 23, -24*a + 20], [a + 1, 1, 1, -5*a - 5, -17*a -
13], [a, -a - 1, 0, 0, -40*a - 25], [a + 1, a, a + 1, 0, -4*a - 3], [a,
a + 1, 0, -6*a - 4, -11*a - 6], [1, 1, 0, -2, 7*a + 3], [0, a, 0, 7*a -
13, 6*a - 12], [0, -a + 1, 0, -7*a - 6, -6*a - 6], [a, -a - 1, a + 1,
-73*a - 44, -308*a - 190], [a, -a - 1, a + 1, -73*a - 44, -308*a - 190],
[1, a - 1, a + 1, 6*a + 2, 2*a + 3], [1, -1, 1, 1, 43*a + 26], [a + 1,
1, a + 1, 27*a + 17, 27*a + 17], [a + 1, a + 1, 0, -104*a - 65, -792*a -
488], [a, -1, 1, -8*a + 15, 45*a - 79], [a + 1, -a - 1, 1, 7*a + 7,
-45*a - 34], [0, -a - 1, a, -4*a - 25, -38*a + 19], [a, a, 0, -3, -5*a -
3], [a + 1, a + 1, 1, 3*a - 3, 3*a - 7], [1, -a, 0, -9*a - 6, a], [a +
1, -a, 1, -61*a - 38, -524*a - 324], [1, -a, 0, -61*a - 38, 81*a + 52],
[0, a - 1, a + 1, -32*a - 21, -116*a - 72], [0, -a, a, 32*a - 53, 115*a
- 187], [0, a - 1, a, -2*a - 11, -8*a - 13], [0, -a - 1, a + 1, -4*a -
1, 4*a + 2], [0, a, a, 17*a - 33, -18*a + 19], [0, -a + 1, a, -17*a -
16, -45*a - 30], [0, -a + 1, a + 1, -17*a - 16, 17*a + 1], [0, -a, 1,
-42*a - 53, -192*a - 140]]
current curve:  [a + 1, -a, 0, 7*a - 23, -24*a + 20]
current curve:  [a + 1, 1, 1, -5*a - 5, -17*a - 13]
current curve:  [1, a - 1, 0, -a, -71*a - 44]
curve:  [1, a - 1, 0, -a, -71*a - 44]  is isomorphic to curve:  [a, a - 1, a + 1, -a, 3*a - 7]
current curve:  [a, -a - 1, 0, 0, -40*a - 25]
current curve:  [a + 1, a, a + 1, 0, -4*a - 3]
curve:  [a + 1, a, a + 1, 0, -4*a - 3]  is isomorphic to curve:  [1, a - 1, 0, -a, -71*a - 44]
current curve:  [a, a + 1, 0, -6*a - 4, -11*a - 6]
curve:  [a, a + 1, 0, -6*a - 4, -11*a - 6]  is isomorphic to curve:  [a + 1, -1, a, -54*a - 33, -63*a - 39]
current curve:  [1, 1, 0, -2, 7*a + 3]
curve:  [1, 1, 0, -2, 7*a + 3]  is isomorphic to curve:  [a + 1, a - 1, a, 7*a - 12, -a + 2]
current curve:  [0, a, 0, 7*a - 13, 6*a - 12]
curve:  [0, a, 0, 7*a - 13, 6*a - 12]  is isomorphic to curve:  [0, -a, 0, -53*a - 33, -126*a - 78]
current curve:  [a, -a - 1, a + 1, -73*a - 44, -308*a - 190]
current curve:  [a, -a - 1, a + 1, -73*a - 44, -308*a - 190]
current curve:  [a, a, a + 1, 39*a + 24, 63*a + 39]
curve:  [a, a, a + 1, 39*a + 24, 63*a + 39]  is isomorphic to curve:  [a + 1, a, 0, 9*a - 9, -7*a + 15]
current curve:  [1, a - 1, a + 1, 6*a + 2, 2*a + 3]
curve:  [1, a - 1, a + 1, 6*a + 2, 2*a + 3]  is isomorphic to curve:  [a, a, a + 1, 39*a + 24, 63*a + 39]
current curve:  [a + 1, 1, a + 1, 27*a + 17, 27*a + 17]
current curve:  [1, -a, 1, -734*a - 454, -11114*a - 6869]
curve:  [1, -a, 1, -734*a - 454, -11114*a - 6869]  is isomorphic to curve:  [a, 1, 0, -13*a - 13, -56*a - 8]
current curve:  [a + 1, a + 1, 0, -104*a - 65, -792*a - 488]
curve:  [a + 1, a + 1, 0, -104*a - 65, -792*a - 488]  is isomorphic to curve:  [1, -a, 1, -734*a - 454, -11114*a - 6869]
current curve:  [a, -1, 1, -8*a + 15, 45*a - 79]
curve:  [a, -1, 1, -8*a + 15, 45*a - 79]  is isomorphic to curve:  [1, -a - 1, 1, 60*a + 37, -855*a - 529]
current curve:  [0, -a - 1, a, -4*a - 25, -38*a + 19]
current curve:  [a + 1, -a + 1, 1, -15*a - 9, -69*a - 43]
curve:  [a + 1, -a + 1, 1, -15*a - 9, -69*a - 43]  is isomorphic to curve:  [1, a - 1, 0, 9*a - 15, -a + 1]
current curve:  [a, a, 0, -3, -5*a - 3]
curve:  [a, a, 0, -3, -5*a - 3]  is isomorphic to curve:  [a + 1, -a + 1, 1, -15*a - 9, -69*a - 43]
current curve:  [a + 1, a + 1, 1, 3*a - 3, 3*a - 7]
curve:  [a + 1, a + 1, 1, 3*a - 3, 3*a - 7]  is isomorphic to curve:  [a, a - 1, a + 1, -66*a - 40, -92*a - 57]
current curve:  [a + 1, -a, 1, -61*a - 38, -524*a - 324]
curve:  [a + 1, -a, 1, -61*a - 38, -524*a - 324]  is isomorphic to curve:  [a, -a + 1, 1, -9*a - 6, -30*a - 17]
current curve:  [1, -a, 0, -61*a - 38, 81*a + 52]
curve:  [1, -a, 0, -61*a - 38, 81*a + 52]  is isomorphic to curve:  [a + 1, a + 1, 1, -5*a - 7, -25*a + 21]
current curve:  [0, a, a + 1, -223*a - 138, -2071*a - 1280]
curve:  [0, a, a + 1, -223*a - 138, -2071*a - 1280]  is isomorphic to curve:  [0, -a, a + 1, 2*a - 13, 7*a - 21]
current curve:  [0, a - 1, a + 1, -32*a - 21, -116*a - 72]
curve:  [0, a - 1, a + 1, -32*a - 21, -116*a - 72]  is isomorphic to curve:  [0, a, a + 1, -223*a - 138, -2071*a - 1280]
current curve:  [0, -a, a, 32*a - 53, 115*a - 187]
curve:  [0, -a, a, 32*a - 53, 115*a - 187]  is isomorphic to curve:  [0, a, a, -43*a - 28, -203*a - 126]
current curve:  [0, 1, a + 1, -30*a - 18, 8*a + 5]
curve:  [0, 1, a + 1, -30*a - 18, 8*a + 5]  is isomorphic to curve:  [0, -1, a + 1, -5*a + 7, 3*a - 6]
current curve:  [0, -a - 1, a + 1, -4*a - 1, 4*a + 2]
curve:  [0, -a - 1, a + 1, -4*a - 1, 4*a + 2]  is isomorphic to curve:  [0, 1, a + 1, -30*a - 18, 8*a + 5]
current curve:  [0, a, a, 17*a - 33, -18*a + 19]
curve:  [0, a, a, 17*a - 33, -18*a + 19]  is isomorphic to curve:  [0, -a, a, -133*a - 83, -820*a - 507]
current curve:  [0, -a, a + 1, -133*a - 83, 242*a + 149]
curve:  [0, -a, a + 1, -133*a - 83, 242*a + 149]  is isomorphic to curve:  [0, a, a + 1, 17*a - 33, 44*a - 75]
current curve:  [0, -a + 1, a + 1, -17*a - 16, 17*a + 1]
curve:  [0, -a + 1, a + 1, -17*a - 16, 17*a + 1]  is isomorphic to curve:  [0, -a, a + 1, -133*a - 83, 242*a + 149]
[[a + 1, -a, 0, 7*a - 23, -24*a + 20], [a + 1, 1, 1, -5*a - 5, -17*a - 13], [a, -a - 1, 0, 0, -40*a - 25], [a + 1, a, a + 1, 0, -4*a - 3], [a, a + 1, 0, -6*a - 4, -11*a - 6], [1, 1, 0, -2, 7*a + 3], [0, a, 0, 7*a - 13, 6*a - 12], [0, -a + 1, 0, -7*a - 6, -6*a - 6], [a, -a - 1, a + 1, -73*a - 44, -308*a - 190], [a, -a - 1, a + 1, -73*a - 44, -308*a - 190], [1, a - 1, a + 1, 6*a + 2, 2*a + 3], [1, -1, 1, 1, 43*a + 26], [a + 1, 1, a + 1, 27*a + 17, 27*a + 17], [a + 1, a + 1, 0, -104*a - 65, -792*a - 488], [a, -1, 1, -8*a + 15, 45*a - 79], [a + 1, -a - 1, 1, 7*a + 7, -45*a - 34], [0, -a - 1, a, -4*a - 25, -38*a + 19], [a, a, 0, -3, -5*a - 3], [a + 1, a + 1, 1, 3*a - 3, 3*a - 7], [1, -a, 0, -9*a - 6, a], [a + 1, -a, 1, -61*a - 38, -524*a - 324], [1, -a, 0, -61*a - 38, 81*a + 52], [0, a - 1, a + 1, -32*a - 21, -116*a - 72], [0, -a, a, 32*a - 53, 115*a - 187], [0, a - 1, a, -2*a - 11, -8*a - 13], [0, -a - 1, a + 1, -4*a - 1, 4*a + 2], [0, a, a, 17*a - 33, -18*a + 19], [0, -a + 1, a, -17*a - 16, -45*a - 30], [0, -a + 1, a + 1, -17*a - 16, 17*a + 1], [0, -a, 1, -42*a - 53, -192*a - 140]]
for i in [[a + 1, -a, 0, 7*a - 23, -24*a + 20], [a + 1, 1, 1, -5*a - 5, -17*a - 13], [a, -a - 1, 0, 0, -40*a - 25], [a + 1, a, a + 1, 0, -4*a - 3], [a, a + 1, 0, -6*a - 4, -11*a - 6], [1, 1, 0, -2, 7*a + 3], [0, a, 0, 7*a - 13, 6*a - 12], [0, -a + 1, 0, -7*a - 6, -6*a - 6], [a, -a - 1, a + 1, -73*a - 44, -308*a - 190], [a, -a - 1, a + 1, -73*a - 44, -308*a - 190], [1, a - 1, a + 1, 6*a + 2, 2*a + 3], [1, -1, 1, 1, 43*a + 26], [a + 1, 1, a + 1, 27*a + 17, 27*a + 17], [a + 1, a + 1, 0, -104*a - 65, -792*a - 488], [a, -1, 1, -8*a + 15, 45*a - 79], [a + 1, -a - 1, 1, 7*a + 7, -45*a - 34], [0, -a - 1, a, -4*a - 25, -38*a + 19], [a, a, 0, -3, -5*a - 3], [a + 1, a + 1, 1, 3*a - 3, 3*a - 7], [1, -a, 0, -9*a - 6, a], [a + 1, -a, 1, -61*a - 38, -524*a - 324], [1, -a, 0, -61*a - 38, 81*a + 52], [0, a - 1, a + 1, -32*a - 21, -116*a - 72], [0, -a, a, 32*a - 53, 115*a - 187], [0, a - 1, a, -2*a - 11, -8*a - 13], [0, -a - 1, a + 1, -4*a - 1, 4*a + 2], [0, a, a, 17*a - 33, -18*a + 19], [0, -a + 1, a, -17*a - 16, -45*a - 30], [0, -a + 1, a + 1, -17*a - 16, 17*a + 1], [0, -a, 1, -42*a - 53, -192*a - 140]]: print i 
        
[a + 1, -a, 0, 7*a - 23, -24*a + 20]
[a + 1, 1, 1, -5*a - 5, -17*a - 13]
[a, -a - 1, 0, 0, -40*a - 25]
[a + 1, a, a + 1, 0, -4*a - 3]
[a, a + 1, 0, -6*a - 4, -11*a - 6]
[1, 1, 0, -2, 7*a + 3]
[0, a, 0, 7*a - 13, 6*a - 12]
[0, -a + 1, 0, -7*a - 6, -6*a - 6]
[a, -a - 1, a + 1, -73*a - 44, -308*a - 190]
[a, -a - 1, a + 1, -73*a - 44, -308*a - 190]
[1, a - 1, a + 1, 6*a + 2, 2*a + 3]
[1, -1, 1, 1, 43*a + 26]
[a + 1, 1, a + 1, 27*a + 17, 27*a + 17]
[a + 1, a + 1, 0, -104*a - 65, -792*a - 488]
[a, -1, 1, -8*a + 15, 45*a - 79]
[a + 1, -a - 1, 1, 7*a + 7, -45*a - 34]
[0, -a - 1, a, -4*a - 25, -38*a + 19]
[a, a, 0, -3, -5*a - 3]
[a + 1, a + 1, 1, 3*a - 3, 3*a - 7]
[1, -a, 0, -9*a - 6, a]
[a + 1, -a, 1, -61*a - 38, -524*a - 324]
[1, -a, 0, -61*a - 38, 81*a + 52]
[0, a - 1, a + 1, -32*a - 21, -116*a - 72]
[0, -a, a, 32*a - 53, 115*a - 187]
[0, a - 1, a, -2*a - 11, -8*a - 13]
[0, -a - 1, a + 1, -4*a - 1, 4*a + 2]
[0, a, a, 17*a - 33, -18*a + 19]
[0, -a + 1, a, -17*a - 16, -45*a - 30]
[0, -a + 1, a + 1, -17*a - 16, 17*a + 1]
[0, -a, 1, -42*a - 53, -192*a - 140]
[a + 1, -a, 0, 7*a - 23, -24*a + 20]
[a + 1, 1, 1, -5*a - 5, -17*a - 13]
[a, -a - 1, 0, 0, -40*a - 25]
[a + 1, a, a + 1, 0, -4*a - 3]
[a, a + 1, 0, -6*a - 4, -11*a - 6]
[1, 1, 0, -2, 7*a + 3]
[0, a, 0, 7*a - 13, 6*a - 12]
[0, -a + 1, 0, -7*a - 6, -6*a - 6]
[a, -a - 1, a + 1, -73*a - 44, -308*a - 190]
[a, -a - 1, a + 1, -73*a - 44, -308*a - 190]
[1, a - 1, a + 1, 6*a + 2, 2*a + 3]
[1, -1, 1, 1, 43*a + 26]
[a + 1, 1, a + 1, 27*a + 17, 27*a + 17]
[a + 1, a + 1, 0, -104*a - 65, -792*a - 488]
[a, -1, 1, -8*a + 15, 45*a - 79]
[a + 1, -a - 1, 1, 7*a + 7, -45*a - 34]
[0, -a - 1, a, -4*a - 25, -38*a + 19]
[a, a, 0, -3, -5*a - 3]
[a + 1, a + 1, 1, 3*a - 3, 3*a - 7]
[1, -a, 0, -9*a - 6, a]
[a + 1, -a, 1, -61*a - 38, -524*a - 324]
[1, -a, 0, -61*a - 38, 81*a + 52]
[0, a - 1, a + 1, -32*a - 21, -116*a - 72]
[0, -a, a, 32*a - 53, 115*a - 187]
[0, a - 1, a, -2*a - 11, -8*a - 13]
[0, -a - 1, a + 1, -4*a - 1, 4*a + 2]
[0, a, a, 17*a - 33, -18*a + 19]
[0, -a + 1, a, -17*a - 16, -45*a - 30]
[0, -a + 1, a + 1, -17*a - 16, 17*a + 1]
[0, -a, 1, -42*a - 53, -192*a - 140]

The curves listed above are the new curves. There turned out to only be 30, but there still could be more if we twist by larger numbers.