UpdatedTwistsChecks

321 days ago by Ben.LeVeque

K.<a> = NumberField(x^2-x-1) 
       
f = open('/Users/bleveque/Sage/minus3,4Twists.txt') g = open('/Users/bleveque/Sage/minus3,4NewCurves.txt','w') 
       
def output_string(line): ainv = eval('['+line.split('(')[1].split(')')[0]+']') N = str(EllipticCurve(K,ainv).conductor().norm()) return N+' '+str(ainv).replace(' ','')+' \n' 
       
for line in f.readlines(): if line[0] == 'N': g.write(output_string(line)) f.close() g.close() 
       
h = open('/Users/bleveque/Sage/minus3,4NewCurves.txt') 
       
for i in h.readlines(): print i 
        
324 [a+1,1,1,-5*a-5,-17*a-13] 

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

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

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

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

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

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

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

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

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

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

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

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

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

775 [0,-a+1,a+1,-17*a-16,17*a+1] 
324 [a+1,1,1,-5*a-5,-17*a-13] 

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

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

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

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

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

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

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

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

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

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

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

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

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

775 [0,-a+1,a+1,-17*a-16,17*a+1]
h = open('/Users/bleveque/Sage/minus3,4NewCurves.txt') 
       
L = [] for line in h.readlines(): L.append(eval('['+line.split('[')[1].split(']')[0]+']')) M = L 
       
for i in L: print i 
        
[a + 1, 1, 1, -5*a - 5, -17*a - 13]
[a, -a - 1, 0, 0, -40*a - 25]
[a, a + 1, 0, -6*a - 4, -11*a - 6]
[a + 1, a - 1, a, 7*a - 12, -a + 2]
[0, -a + 1, 0, -7*a - 6, -6*a - 6]
[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, a, 0, -3, -5*a - 3]
[a, -a + 1, 1, -9*a - 6, -30*a - 17]
[a + 1, a + 1, 1, -5*a - 7, -25*a + 21]
[0, a - 1, a + 1, -32*a - 21, -116*a - 72]
[0, a - 1, a, -2*a - 11, -8*a - 13]
[0, -a - 1, a + 1, -4*a - 1, 4*a + 2]
[0, -a + 1, a, -17*a - 16, -45*a - 30]
[0, -a + 1, a + 1, -17*a - 16, 17*a + 1]
[a + 1, 1, 1, -5*a - 5, -17*a - 13]
[a, -a - 1, 0, 0, -40*a - 25]
[a, a + 1, 0, -6*a - 4, -11*a - 6]
[a + 1, a - 1, a, 7*a - 12, -a + 2]
[0, -a + 1, 0, -7*a - 6, -6*a - 6]
[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, a, 0, -3, -5*a - 3]
[a, -a + 1, 1, -9*a - 6, -30*a - 17]
[a + 1, a + 1, 1, -5*a - 7, -25*a + 21]
[0, a - 1, a + 1, -32*a - 21, -116*a - 72]
[0, a - 1, a, -2*a - 11, -8*a - 13]
[0, -a - 1, a + 1, -4*a - 1, 4*a + 2]
[0, -a + 1, a, -17*a - 16, -45*a - 30]
[0, -a + 1, a + 1, -17*a - 16, 17*a + 1]

Double-check for repeats:
check = [] for Lainvs in L: E = EllipticCurve(K,Lainvs) for Mainvs in M: c='hi' c if Lainvs != Mainvs: F = EllipticCurve(K,Mainvs) if E.is_isomorphic(F) or E.is_isogenous(F): print Lainvs, 'related to', Mainvs check.append(Lainvs) if check == []: print 'No repeats' 
        
No repeats
No repeats
j = open('/Users/bleveque/Sage/matched1000.txt') 
       
check = [] for Lainvs in L: E = EllipticCurve(K,Lainvs) for line in j.readlines(): jainvs = eval('['+line.split('[')[1].split(']')[0]+']') F = EllipticCurve(K,jainvs) if E.is_isomorphic(F) or E.is_isogenous(F): print Lainvs, 'related to', jainvs check.append(Lainvs) if check == []: print 'No repeats' 
        
No repeats
No repeats