Mod-Jon_Code_9-10-11

1856 -8*a + 48 
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1805 -a + 43 [1,2,'?',2,0,0,'?',-4,6,6,8,4,6,-6,-12,12,-14,10,0,-12,8,16,-6,-6][a + 1, -a + 1, a + 1, -62*a - 86, -411*a - 311]

899

52.1500000000000

451

[3, 1, -1, 4, 0, '?', -6, 1, -6, 2, 4, 0, '?', 0, -1, 2, -3, 6, -6, -12, 11, 14, -3, -16]

549

[3, '?', -1, 3, -3, 3, -2, 7, -6, 1, 3, -5, -2, 6, 6, -14, -11, '?', -8, -5, 14, 0, -1, -10]

781

[1, 2, 2, -2, '?', -4, 8, 4, -2, 6, -4, -8, 10, -2, -12, 0, 2, -2, -12, '?', 4, 8, -6, -6]

836

['?', -4, 2, -4, 4, '?', '?', -2, 4, 8, 10, 0, -4, -4, -14, -12, -2, -2, -4, 0, 4, -16, 14, -10]

836

['?', 2, 1, 0, 4, '?', -2, '?', -2, 4, 7, 4, -5, 9, 0, -11, -1, -2, 6, -7, -2, 8, 7, -8]

False

Elliptic Curve defined by y^2 = x^3 + 4*x + 1 over Residue field of Fractional ideal (3*a - 2)

Elliptic Curve defined by y^2 = x^3 + 8*x + 1 over Residue field of Fractional ideal (3*a - 2)

Elliptic Curve defined by y^2 = x^3 + 8*x + 1 over Residue field of Fractional ideal (3*a - 1)

(11*a, -22*a - 22, 22*a + 11, -109*a - 66, -11*a + 1)

1

8

179 -12*a + 5 
Traceback (most recent call last):        print S[0]
  File "", line 1, in <module>
    
  File "/private/var/folders/+3/+3+bRf7bGhaMk-2vvrWEvU+++TI/-Tmp-/tmp9S8hAv/___code___.py", line 5, in <module>
    exec compile(u"for s in f.readlines():\n    S = s.split('[')\n    aps = eval('['+S[_sage_const_1 ])\n    aps = aps[_sage_const_4 :]\n    print S[_sage_const_0 ]\n    t = S[_sage_const_0 ].split(' ')\n    cond = eval(''.join(t[_sage_const_1 :]))\n    E = curve_finder(cond,aps)\n    g = open('/Users/bleveque/Sage/modjon728/output%s.txt'%i,'w')\n    if E is None:\n        g.write(s)\n        g.write(' unfound\\n')\n    else:\n        g.write(s[:-_sage_const_1 ])\n        g.write(' '+str(list(E.ainvs()))+'\\n')\n    g.close()\n    i += _sage_const_1 " + '\n', '', 'single')
  File "", line 7, in <module>
    
  File "<string>", line 1, in <module>
NameError: name 'a' is not defined

22

Elliptic Curve defined by y^2 + (a+1)*x*y + a*y = x^3 + x^2 + (-15*a-11)*x + (-50*a-33) over Number Field in a with defining polynomial x^2 - x - 1

Fractional ideal (-12*a + 5)

0

current prime =  11
current prime =  19
(-a + 1, -a, 0, -4, 5*a - 2) tentative
(-a + 2, -a + 1, 0, -3*a + 5, 0) tentative
(-a + 1, -a, 0, 1, 0) tentative
current prime =  29
(a, a, 1, -8*a - 16, 25*a + 2) tentative
(1, a - 1, -a + 2, a, 3*a) tentative
current prime =  31
current prime =  41
current prime =  59
(10000L, 'of', 40368L, '---', 59L)
(20000L, 'of', 40368L, '---', 59L)
(-a + 2, -a + 2, 0, -11*a - 12, 40*a - 4) tentative
(30000L, 'of', 40368L, '---', 59L)
(40000L, 'of', 40368L, '---', 59L)
current prime =  61
(10000L, 'of', 43200L, '---', 61L)
(20000L, 'of', 43200L, '---', 61L)
(30000L, 'of', 43200L, '---', 61L)
(-a + 1, 0, -a + 1, a - 1, a) tentative
(40000L, 'of', 43200L, '---', 61L)
(-a + 2, -a + 2, 0, -11*a - 12, 40*a - 4) tentative
current prime =  71
(10000L, 'of', 19600L, '---', 71L)
(a, a, 1, -8*a - 16, 25*a + 2) tentative
current prime =  79
(10000L, 'of', 56784L, '---', 79L)
(20000L, 'of', 56784L, '---', 79L)
(30000L, 'of', 56784L, '---', 79L)
(-a + 2, -a + 2, 0, -11*a - 12, 40*a - 4) tentative
(40000L, 'of', 56784L, '---', 79L)
(50000L, 'of', 56784L, '---', 79L)
current prime =  89
(10000L, 'of', 108416L, '---', 89L)
(20000L, 'of', 108416L, '---', 89L)
(30000L, 'of', 108416L, '---', 89L)
(40000L, 'of', 108416L, '---', 89L)
(50000L, 'of', 108416L, '---', 89L)
(60000L, 'of', 108416L, '---', 89L)
(70000L, 'of', 108416L, '---', 89L)
(80000L, 'of', 108416L, '---', 89L)
(90000L, 'of', 108416L, '---', 89L)
(100000L, 'of', 108416L, '---', 89L)
CPU time: 209.05 s,  Wall time: 211.04 s

[0, -2, 4, -4, -6, -8, -6, 10, '?', 10, 4, 12, 2, 6, 4, -2, -4, -16, -8, -6]

Fractional ideal (-13*a + 4)

Fractional ideal (13*a - 9)

[0, -2, 4, -4, -6, -8, -6, 10, '?', 10, 4, 12, 2, 6, 4, -2, -4, -16, -8, -6]
[-2, 0, -4, 4, -8, -6, 10, -6, '?', '?', 12, 4, 6, 2, -2, 4, -16, -4, -6, -8]

current prime =  11
current prime =  19
current prime =  29
current prime =  31
(-a + 1, -a, -a + 1, 5*a - 23, -24*a + 23) tentative
(-a + 1, -a, -a + 1, 5*a - 23, -24*a + 23) a_ps match

599 Fractional ideal (a + 24)
-4

current prime =  11
current prime =  19
Elliptic Curve defined by y^2 + (a+1)*x*y + y = x^3 + (a+1)*x^2 + (5*a-9)*x + (3*a-16) over Number Field in a with defining polynomial x^2 - x - 1 tentative
Elliptic Curve defined by y^2 + (a+1)*x*y + y = x^3 + (a+1)*x^2 + (5*a-9)*x + (3*a-16) over Number Field in a with defining polynomial x^2 - x - 1 a_ps match
singular curve
current prime =  29
Elliptic Curve defined by y^2 + (a+1)*x*y + y = x^3 + (a+1)*x^2 + (5*a-9)*x + (3*a-16) over Number Field in a with defining polynomial x^2 - x - 1 tentative
Elliptic Curve defined by y^2 + (a+1)*x*y + y = x^3 + (a+1)*x^2 + (5*a-9)*x + (3*a-16) over Number Field in a with defining polynomial x^2 - x - 1 a_ps match
singular curve
current prime =  31
Elliptic Curve defined by y^2 + (a+1)*x*y + y = x^3 + (a+1)*x^2 + (5*a-9)*x + (3*a-16) over Number Field in a with defining polynomial x^2 - x - 1 tentative
Elliptic Curve defined by y^2 + (a+1)*x*y + y = x^3 + (a+1)*x^2 + (5*a-9)*x + (3*a-16) over Number Field in a with defining polynomial x^2 - x - 1 a_ps match
Elliptic Curve defined by y^2 + (a+1)*x*y + y = x^3 + (a+1)*x^2 + (5*a-9)*x + (3*a-16) over Number Field in a with defining polynomial x^2 - x - 1 tentative
Elliptic Curve defined by y^2 + (a+1)*x*y + y = x^3 + (a+1)*x^2 + (5*a-9)*x + (3*a-16) over Number Field in a with defining polynomial x^2 - x - 1 a_ps match
current prime =  41
Elliptic Curve defined by y^2 + (a+1)*x*y + y = x^3 + (a+1)*x^2 + (5*a-9)*x + (3*a-16) over Number Field in a with defining polynomial x^2 - x - 1 tentative
Elliptic Curve defined by y^2 + (a+1)*x*y + y = x^3 + (a+1)*x^2 + (5*a-9)*x + (3*a-16) over Number Field in a with defining polynomial x^2 - x - 1 a_ps match
singular curve
current prime =  59
Elliptic Curve defined by y^2 + (a+1)*x*y + y = x^3 + (a+1)*x^2 + (5*a-9)*x + (3*a-16) over Number Field in a with defining polynomial x^2 - x - 1 tentative
Elliptic Curve defined by y^2 + (a+1)*x*y + y = x^3 + (a+1)*x^2 + (5*a-9)*x + (3*a-16) over Number Field in a with defining polynomial x^2 - x - 1 a_ps match
current prime =  61
singular curve
Elliptic Curve defined by y^2 + (a+1)*x*y + y = x^3 + (a+1)*x^2 + (5*a-9)*x + (3*a-16) over Number Field in a with defining polynomial x^2 - x - 1 tentative
Elliptic Curve defined by y^2 + (a+1)*x*y + y = x^3 + (a+1)*x^2 + (5*a-9)*x + (3*a-16) over Number Field in a with defining polynomial x^2 - x - 1 a_ps match
current prime =  71
current prime =  79
singular curve
singular curve
singular curve
Elliptic Curve defined by y^2 + (a+1)*x*y + y = x^3 + (a+1)*x^2 + (5*a-9)*x + (3*a-16) over Number Field in a with defining polynomial x^2 - x - 1 tentative
Elliptic Curve defined by y^2 + (a+1)*x*y + y = x^3 + (a+1)*x^2 + (5*a-9)*x + (3*a-16) over Number Field in a with defining polynomial x^2 - x - 1 a_ps match
current prime =  89
singular curve
Elliptic Curve defined by y^2 + (a+1)*x*y + y = x^3 + (a+1)*x^2 + (5*a-9)*x + (3*a-16) over Number Field in a with defining polynomial x^2 - x - 1 tentative
Elliptic Curve defined by y^2 + (a+1)*x*y + y = x^3 + (a+1)*x^2 + (5*a-9)*x + (3*a-16) over Number Field in a with defining polynomial x^2 - x - 1 a_ps match

284 Fractional ideal (2*a + 16)
-2

current prime =  11
current prime =  19
current prime =  29
singular curve
singular curve
singular curve
current prime =  31
singular curve
singular curve
singular curve
singular curve
singular curve
singular curve
singular curve
current prime =  41
current prime =  59
singular curve
singular curve
singular curve
singular curve
singular curve
singular curve
singular curve
singular curve
singular curve
current prime =  61
singular curve
current prime =  71
singular curve
singular curve
singular curve
singular curve
singular curve
singular curve
current prime =  79
Elliptic Curve defined by y^2 + (a+1)*x*y = x^3 + (a+1)*x^2 + (-12*a+6)*x + (-76*a+64) over Number Field in a with defining polynomial x^2 - x - 1 tentative
current prime =  89
singular curve
singular curve
singular curve
Elliptic Curve defined by y^2 + (a+1)*x*y = x^3 + (a+1)*x^2 + (-12*a+6)*x + (-76*a+64) over Number Field in a with defining polynomial x^2 - x - 1 tentative

Fractional ideal (-4*a - 18)
4

current prime =  11
singular curve
Elliptic Curve defined by y^2 + x*y = x^3 + (2*a-7)*x + (3*a-8) over Number Field in a with defining polynomial x^2 - x - 1 tentative
current prime =  19
Elliptic Curve defined by y^2 + x*y = x^3 + (2*a-7)*x + (3*a-8) over Number Field in a with defining polynomial x^2 - x - 1 tentative
singular curve
singular curve
singular curve
Elliptic Curve defined by y^2 + x*y = x^3 + (2*a-7)*x + (3*a-8) over Number Field in a with defining polynomial x^2 - x - 1 tentative
singular curve
singular curve
singular curve
current prime =  29
Elliptic Curve defined by y^2 + a*x*y = x^3 + (-11*a-8)*x + (-25*a-16) over Number Field in a with defining polynomial x^2 - x - 1 tentative
Elliptic Curve defined by y^2 + x*y = x^3 + (2*a-7)*x + (3*a-8) over Number Field in a with defining polynomial x^2 - x - 1 tentative
singular curve
current prime =  31
Elliptic Curve defined by y^2 + a*x*y = x^3 + (-11*a-8)*x + (-25*a-16) over Number Field in a with defining polynomial x^2 - x - 1 tentative
Elliptic Curve defined by y^2 + x*y = x^3 + (2*a-7)*x + (3*a-8) over Number Field in a with defining polynomial x^2 - x - 1 tentative
singular curve
singular curve
singular curve
current prime =  41
singular curve
singular curve
singular curve
Elliptic Curve defined by y^2 + x*y = x^3 + (2*a-7)*x + (3*a-8) over Number Field in a with defining polynomial x^2 - x - 1 tentative
singular curve
Elliptic Curve defined by y^2 + a*x*y = x^3 + (-6*a-23)*x + (2*a-32) over Number Field in a with defining polynomial x^2 - x - 1 tentative
Elliptic Curve defined by y^2 + a*x*y = x^3 + (-11*a-8)*x + (-25*a-16) over Number Field in a with defining polynomial x^2 - x - 1 tentative
singular curve
current prime =  59
Elliptic Curve defined by y^2 + a*x*y = x^3 + (-11*a-8)*x + (-25*a-16) over Number Field in a with defining polynomial x^2 - x - 1 tentative
Elliptic Curve defined by y^2 + x*y = x^3 + (2*a-7)*x + (3*a-8) over Number Field in a with defining polynomial x^2 - x - 1 tentative
Elliptic Curve defined by y^2 + a*x*y = x^3 + (-6*a-23)*x + (2*a-32) over Number Field in a with defining polynomial x^2 - x - 1 tentative
current prime =  61
Elliptic Curve defined by y^2 + x*y = x^3 + (2*a-7)*x + (3*a-8) over Number Field in a with defining polynomial x^2 - x - 1 tentative
Elliptic Curve defined by y^2 + a*x*y = x^3 + (-11*a-8)*x + (-25*a-16) over Number Field in a with defining polynomial x^2 - x - 1 tentative
singular curve
Elliptic Curve defined by y^2 + a*x*y = x^3 + (-6*a-23)*x + (2*a-32) over Number Field in a with defining polynomial x^2 - x - 1 tentative
singular curve
singular curve
current prime =  71
singular curve
singular curve
Elliptic Curve defined by y^2 + x*y = x^3 + (2*a-7)*x + (3*a-8) over Number Field in a with defining polynomial x^2 - x - 1 tentative
Elliptic Curve defined by y^2 + a*x*y = x^3 + (-11*a-8)*x + (-25*a-16) over Number Field in a with defining polynomial x^2 - x - 1 tentative
Elliptic Curve defined by y^2 + a*x*y = x^3 + (-6*a-23)*x + (2*a-32) over Number Field in a with defining polynomial x^2 - x - 1 tentative
current prime =  79
current prime =  89
Elliptic Curve defined by y^2 + a*x*y = x^3 + (-6*a-23)*x + (2*a-32) over Number Field in a with defining polynomial x^2 - x - 1 tentative
singular curve
singular curve
Elliptic Curve defined by y^2 + x*y = x^3 + (2*a-7)*x + (3*a-8) over Number Field in a with defining polynomial x^2 - x - 1 tentative
singular curve
Elliptic Curve defined by y^2 + a*x*y = x^3 + (-11*a-8)*x + (-25*a-16) over Number Field in a with defining polynomial x^2 - x - 1 tentative
Elliptic Curve defined by y^2 + a*x*y = x^3 + (-6*a-23)*x + (2*a-32) over Number Field in a with defining polynomial x^2 - x - 1 tentative
singular curve
singular curve
Elliptic Curve defined by y^2 + x*y = x^3 + (2*a-7)*x + (3*a-8) over Number Field in a with defining polynomial x^2 - x - 1 tentative
singular curve
Elliptic Curve defined by y^2 + a*x*y = x^3 + (-11*a-8)*x + (-25*a-16) over Number Field in a with defining polynomial x^2 - x - 1 tentative

Fractional ideal (2*a + 19) Fractional ideal (2*a + 19) Fractional ideal (2*a + 19)
0 0 0

current prime =  11
current prime =  19
Elliptic Curve defined by y^2 + (a+1)*x*y = x^3 + (-a-1)*x^2 + (-a-3)*x + (2*a-9) over Number Field in a with defining polynomial x^2 - x - 1 tentative
Elliptic Curve defined by y^2 + (a+1)*x*y = x^3 + (-a-1)*x^2 + (-a-3)*x + (2*a-9) over Number Field in a with defining polynomial x^2 - x - 1 a_ps match
current prime =  29
Elliptic Curve defined by y^2 + (a+1)*x*y = x^3 + (-a-1)*x^2 + (-a-3)*x + (2*a-9) over Number Field in a with defining polynomial x^2 - x - 1 tentative
Elliptic Curve defined by y^2 + (a+1)*x*y = x^3 + (-a-1)*x^2 + (-a-3)*x + (2*a-9) over Number Field in a with defining polynomial x^2 - x - 1 a_ps match
current prime =  31
Elliptic Curve defined by y^2 + (a+1)*x*y = x^3 + (-a-1)*x^2 + (-a-3)*x + (2*a-9) over Number Field in a with defining polynomial x^2 - x - 1 tentative
Elliptic Curve defined by y^2 + (a+1)*x*y = x^3 + (-a-1)*x^2 + (-a-3)*x + (2*a-9) over Number Field in a with defining polynomial x^2 - x - 1 a_ps match
current prime =  41
singular curve
Elliptic Curve defined by y^2 + (a+1)*x*y = x^3 + (-a-1)*x^2 + (-a-3)*x + (2*a-9) over Number Field in a with defining polynomial x^2 - x - 1 tentative
Elliptic Curve defined by y^2 + (a+1)*x*y = x^3 + (-a-1)*x^2 + (-a-3)*x + (2*a-9) over Number Field in a with defining polynomial x^2 - x - 1 a_ps match
singular curve
current prime =  59
Elliptic Curve defined by y^2 + (a+1)*x*y = x^3 + (-a-1)*x^2 + (-a-3)*x + (2*a-9) over Number Field in a with defining polynomial x^2 - x - 1 tentative
Elliptic Curve defined by y^2 + (a+1)*x*y = x^3 + (-a-1)*x^2 + (-a-3)*x + (2*a-9) over Number Field in a with defining polynomial x^2 - x - 1 a_ps match
current prime =  61
Elliptic Curve defined by y^2 + (a+1)*x*y = x^3 + (-a-1)*x^2 + (-a-3)*x + (2*a-9) over Number Field in a with defining polynomial x^2 - x - 1 tentative
Elliptic Curve defined by y^2 + (a+1)*x*y = x^3 + (-a-1)*x^2 + (-a-3)*x + (2*a-9) over Number Field in a with defining polynomial x^2 - x - 1 a_ps match
current prime =  71
Elliptic Curve defined by y^2 + (a+1)*x*y = x^3 + (-a-1)*x^2 + (-a-3)*x + (2*a-9) over Number Field in a with defining polynomial x^2 - x - 1 tentative
Elliptic Curve defined by y^2 + (a+1)*x*y = x^3 + (-a-1)*x^2 + (-a-3)*x + (2*a-9) over Number Field in a with defining polynomial x^2 - x - 1 a_ps match
current prime =  79
Elliptic Curve defined by y^2 + (a+1)*x*y = x^3 + (-a-1)*x^2 + (-a-3)*x + (2*a-9) over Number Field in a with defining polynomial x^2 - x - 1 tentative
Elliptic Curve defined by y^2 + (a+1)*x*y = x^3 + (-a-1)*x^2 + (-a-3)*x + (2*a-9) over Number Field in a with defining polynomial x^2 - x - 1 a_ps match
Elliptic Curve defined by y^2 + (a+1)*x*y = x^3 + (-a-1)*x^2 + (-a-3)*x + (2*a-9) over Number Field in a with defining polynomial x^2 - x - 1 tentative
Elliptic Curve defined by y^2 + (a+1)*x*y = x^3 + (-a-1)*x^2 + (-a-3)*x + (2*a-9) over Number Field in a with defining polynomial x^2 - x - 1 a_ps match
current prime =  89
Elliptic Curve defined by y^2 + (a+1)*x*y = x^3 + (-a-1)*x^2 + (-a-3)*x + (2*a-9) over Number Field in a with defining polynomial x^2 - x - 1 tentative
Elliptic Curve defined by y^2 + (a+1)*x*y = x^3 + (-a-1)*x^2 + (-a-3)*x + (2*a-9) over Number Field in a with defining polynomial x^2 - x - 1 a_ps match

396 Fractional ideal (18*a - 12)
7

current prime =  11
singular curve
singular curve
singular curve
current prime =  19
singular curve
singular curve
singular curve
current prime =  29
singular curve
singular curve
singular curve
singular curve
singular curve
current prime =  31
singular curve
current prime =  41
singular curve
current prime =  59
Elliptic Curve defined by y^2 + (a+1)*x*y + a*y = x^3 + (48*a+28)*x + (13*a+7) over Number Field in a with defining polynomial x^2 - x - 1 tentative
current prime =  61
Elliptic Curve defined by y^2 + (a+1)*x*y + a*y = x^3 + (48*a+28)*x + (13*a+7) over Number Field in a with defining polynomial x^2 - x - 1 tentative
current prime =  71
Elliptic Curve defined by y^2 + (a+1)*x*y + a*y = x^3 + (48*a+28)*x + (13*a+7) over Number Field in a with defining polynomial x^2 - x - 1 tentative
current prime =  79
Elliptic Curve defined by y^2 + (a+1)*x*y + a*y = x^3 + (48*a+28)*x + (13*a+7) over Number Field in a with defining polynomial x^2 - x - 1 tentative
singular curve
current prime =  89
singular curve
Elliptic Curve defined by y^2 + (a+1)*x*y + a*y = x^3 + (48*a+28)*x + (13*a+7) over Number Field in a with defining polynomial x^2 - x - 1 tentative

404 Fractional ideal (18*a - 10)
-2

current prime =  11
Elliptic Curve defined by y^2 + (a+1)*x*y + (a+1)*y = x^3 + x^2 + (-a-6)*x + (-3*a-9) over Number Field in a with defining polynomial x^2 - x - 1 tentative
Elliptic Curve defined by y^2 + (a+1)*x*y + (a+1)*y = x^3 + x^2 + (-a-6)*x + (-3*a-9) over Number Field in a with defining polynomial x^2 - x - 1 a_ps match
current prime =  19
Elliptic Curve defined by y^2 + (a+1)*x*y + (a+1)*y = x^3 + x^2 + (-a-6)*x + (-3*a-9) over Number Field in a with defining polynomial x^2 - x - 1 tentative
Elliptic Curve defined by y^2 + (a+1)*x*y + (a+1)*y = x^3 + x^2 + (-a-6)*x + (-3*a-9) over Number Field in a with defining polynomial x^2 - x - 1 a_ps match
singular curve
current prime =  29
Elliptic Curve defined by y^2 + (a+1)*x*y + (a+1)*y = x^3 + x^2 + (-a-6)*x + (-3*a-9) over Number Field in a with defining polynomial x^2 - x - 1 tentative
Elliptic Curve defined by y^2 + (a+1)*x*y + (a+1)*y = x^3 + x^2 + (-a-6)*x + (-3*a-9) over Number Field in a with defining polynomial x^2 - x - 1 a_ps match
current prime =  31
Elliptic Curve defined by y^2 + (a+1)*x*y + (a+1)*y = x^3 + x^2 + (-a-6)*x + (-3*a-9) over Number Field in a with defining polynomial x^2 - x - 1 tentative
Elliptic Curve defined by y^2 + (a+1)*x*y + (a+1)*y = x^3 + x^2 + (-a-6)*x + (-3*a-9) over Number Field in a with defining polynomial x^2 - x - 1 a_ps match
current prime =  41
singular curve
Elliptic Curve defined by y^2 + (a+1)*x*y + (a+1)*y = x^3 + x^2 + (-a-6)*x + (-3*a-9) over Number Field in a with defining polynomial x^2 - x - 1 tentative
Elliptic Curve defined by y^2 + (a+1)*x*y + (a+1)*y = x^3 + x^2 + (-a-6)*x + (-3*a-9) over Number Field in a with defining polynomial x^2 - x - 1 a_ps match
singular curve
singular curve
singular curve
current prime =  59
singular curve
Elliptic Curve defined by y^2 + (a+1)*x*y + (a+1)*y = x^3 + x^2 + (-a-6)*x + (-3*a-9) over Number Field in a with defining polynomial x^2 - x - 1 tentative
Elliptic Curve defined by y^2 + (a+1)*x*y + (a+1)*y = x^3 + x^2 + (-a-6)*x + (-3*a-9) over Number Field in a with defining polynomial x^2 - x - 1 a_ps match
current prime =  61
singular curve
Elliptic Curve defined by y^2 + x*y = x^3 + (-1)*x^2 + (-20*a-13)*x + (-50*a-31) over Number Field in a with defining polynomial x^2 - x - 1 tentative
Elliptic Curve defined by y^2 + x*y = x^3 + (-1)*x^2 + (-20*a-13)*x + (-50*a-31) over Number Field in a with defining polynomial x^2 - x - 1 a_ps match
current prime =  71
Elliptic Curve defined by y^2 + (a+1)*x*y + (a+1)*y = x^3 + x^2 + (-a-6)*x + (-3*a-9) over Number Field in a with defining polynomial x^2 - x - 1 tentative
Elliptic Curve defined by y^2 + (a+1)*x*y + (a+1)*y = x^3 + x^2 + (-a-6)*x + (-3*a-9) over Number Field in a with defining polynomial x^2 - x - 1 a_ps match
current prime =  79
Elliptic Curve defined by y^2 + (a+1)*x*y + (a+1)*y = x^3 + x^2 + (-a-6)*x + (-3*a-9) over Number Field in a with defining polynomial x^2 - x - 1 tentative
Elliptic Curve defined by y^2 + (a+1)*x*y + (a+1)*y = x^3 + x^2 + (-a-6)*x + (-3*a-9) over Number Field in a with defining polynomial x^2 - x - 1 a_ps match
current prime =  89
Elliptic Curve defined by y^2 + x*y = x^3 + (-1)*x^2 + (-20*a-13)*x + (-50*a-31) over Number Field in a with defining polynomial x^2 - x - 1 tentative
Elliptic Curve defined by y^2 + x*y = x^3 + (-1)*x^2 + (-20*a-13)*x + (-50*a-31) over Number Field in a with defining polynomial x^2 - x - 1 a_ps match

404 Fractional ideal (18*a - 8)
4

current prime =  11
singular curve
singular curve
singular curve
singular curve
singular curve
singular curve
singular curve
singular curve
singular curve
singular curve
singular curve
singular curve
singular curve
singular curve
current prime =  19
singular curve
current prime =  29
Elliptic Curve defined by y^2 + (a+1)*x*y + (a+1)*y = x^3 + (-1)*x^2 + (-7*a-7)*x + (-12*a-8) over Number Field in a with defining polynomial x^2 - x - 1 tentative
Elliptic Curve defined by y^2 + x*y + (a+1)*y = x^3 + a*x^2 + (-6*a-4)*x over Number Field in a with defining polynomial x^2 - x - 1 tentative
Elliptic Curve defined by y^2 = x^3 + x^2 + (-7*a-20)*x + (3*a+20) over Number Field in a with defining polynomial x^2 - x - 1 tentative
Elliptic Curve defined by y^2 + (a+1)*x*y + (a+1)*y = x^3 + (-1)*x^2 + (-2*a-2)*x + (-a) over Number Field in a with defining polynomial x^2 - x - 1 tentative
current prime =  31
singular curve
singular curve
singular curve
singular curve
singular curve
singular curve
singular curve
current prime =  41
singular curve
current prime =  59
singular curve
singular curve
singular curve
singular curve
Elliptic Curve defined by y^2 + a*x*y + (a+1)*y = x^3 + x^2 + (-23*a-16)*x + (52*a+30) over Number Field in a with defining polynomial x^2 - x - 1 tentative
Elliptic Curve defined by y^2 + a*x*y + (a+1)*y = x^3 + x^2 + (-23*a-16)*x + (52*a+30) over Number Field in a with defining polynomial x^2 - x - 1 a_ps match

445 Fractional ideal (-19*a + 7)
-8

current prime =  11
current prime =  19
Elliptic Curve defined by y^2 + (a+1)*x*y = x^3 + x^2 + (-2*a-2)*x + (-16*a-12) over Number Field in a with defining polynomial x^2 - x - 1 tentative
Elliptic Curve defined by y^2 + (a+1)*x*y = x^3 + x^2 + (-2*a-2)*x + (-16*a-12) over Number Field in a with defining polynomial x^2 - x - 1 a_ps match
Elliptic Curve defined by y^2 + (a+1)*x*y = x^3 + x^2 + (-2*a-2)*x + (-16*a-12) over Number Field in a with defining polynomial x^2 - x - 1 tentative
Elliptic Curve defined by y^2 + (a+1)*x*y = x^3 + x^2 + (-2*a-2)*x + (-16*a-12) over Number Field in a with defining polynomial x^2 - x - 1 a_ps match
current prime =  29
singular curve
Elliptic Curve defined by y^2 + (a+1)*x*y = x^3 + x^2 + (-2*a-2)*x + (-16*a-12) over Number Field in a with defining polynomial x^2 - x - 1 tentative
Elliptic Curve defined by y^2 + (a+1)*x*y = x^3 + x^2 + (-2*a-2)*x + (-16*a-12) over Number Field in a with defining polynomial x^2 - x - 1 a_ps match
singular curve
Elliptic Curve defined by y^2 + (a+1)*x*y = x^3 + x^2 + (-2*a-2)*x + (-16*a-12) over Number Field in a with defining polynomial x^2 - x - 1 tentative
Elliptic Curve defined by y^2 + (a+1)*x*y = x^3 + x^2 + (-2*a-2)*x + (-16*a-12) over Number Field in a with defining polynomial x^2 - x - 1 a_ps match
current prime =  31
Elliptic Curve defined by y^2 + (a+1)*x*y = x^3 + x^2 + (-2*a-2)*x + (-16*a-12) over Number Field in a with defining polynomial x^2 - x - 1 tentative
Elliptic Curve defined by y^2 + (a+1)*x*y = x^3 + x^2 + (-2*a-2)*x + (-16*a-12) over Number Field in a with defining polynomial x^2 - x - 1 a_ps match
Elliptic Curve defined by y^2 + (a+1)*x*y = x^3 + x^2 + (-2*a-2)*x + (-16*a-12) over Number Field in a with defining polynomial x^2 - x - 1 tentative
Elliptic Curve defined by y^2 + (a+1)*x*y = x^3 + x^2 + (-2*a-2)*x + (-16*a-12) over Number Field in a with defining polynomial x^2 - x - 1 a_ps match
current prime =  41
Elliptic Curve defined by y^2 + (a+1)*x*y = x^3 + x^2 + (-2*a-2)*x + (-16*a-12) over Number Field in a with defining polynomial x^2 - x - 1 tentative
Elliptic Curve defined by y^2 + (a+1)*x*y = x^3 + x^2 + (-2*a-2)*x + (-16*a-12) over Number Field in a with defining polynomial x^2 - x - 1 a_ps match
Elliptic Curve defined by y^2 + (a+1)*x*y = x^3 + x^2 + (-2*a-2)*x + (-16*a-12) over Number Field in a with defining polynomial x^2 - x - 1 tentative
Elliptic Curve defined by y^2 + (a+1)*x*y = x^3 + x^2 + (-2*a-2)*x + (-16*a-12) over Number Field in a with defining polynomial x^2 - x - 1 a_ps match
current prime =  59
singular curve
singular curve
singular curve
Elliptic Curve defined by y^2 + (a+1)*x*y = x^3 + x^2 + (-2*a-2)*x + (-16*a-12) over Number Field in a with defining polynomial x^2 - x - 1 tentative
Elliptic Curve defined by y^2 + (a+1)*x*y = x^3 + x^2 + (-2*a-2)*x + (-16*a-12) over Number Field in a with defining polynomial x^2 - x - 1 a_ps match
singular curve
singular curve
singular curve
Elliptic Curve defined by y^2 + (a+1)*x*y = x^3 + x^2 + (-2*a-2)*x + (-16*a-12) over Number Field in a with defining polynomial x^2 - x - 1 tentative
Elliptic Curve defined by y^2 + (a+1)*x*y = x^3 + x^2 + (-2*a-2)*x + (-16*a-12) over Number Field in a with defining polynomial x^2 - x - 1 a_ps match
current prime =  61
Elliptic Curve defined by y^2 + (a+1)*x*y = x^3 + x^2 + (-2*a-2)*x + (-16*a-12) over Number Field in a with defining polynomial x^2 - x - 1 tentative
Elliptic Curve defined by y^2 + (a+1)*x*y = x^3 + x^2 + (-2*a-2)*x + (-16*a-12) over Number Field in a with defining polynomial x^2 - x - 1 a_ps match
Elliptic Curve defined by y^2 + (a+1)*x*y = x^3 + x^2 + (-2*a-2)*x + (-16*a-12) over Number Field in a with defining polynomial x^2 - x - 1 tentative
Elliptic Curve defined by y^2 + (a+1)*x*y = x^3 + x^2 + (-2*a-2)*x + (-16*a-12) over Number Field in a with defining polynomial x^2 - x - 1 a_ps match
current prime =  71
Elliptic Curve defined by y^2 + (a+1)*x*y = x^3 + x^2 + (-2*a-2)*x + (-16*a-12) over Number Field in a with defining polynomial x^2 - x - 1 tentative
Elliptic Curve defined by y^2 + (a+1)*x*y = x^3 + x^2 + (-2*a-2)*x + (-16*a-12) over Number Field in a with defining polynomial x^2 - x - 1 a_ps match
Elliptic Curve defined by y^2 + (a+1)*x*y = x^3 + x^2 + (-2*a-2)*x + (-16*a-12) over Number Field in a with defining polynomial x^2 - x - 1 tentative
Elliptic Curve defined by y^2 + (a+1)*x*y = x^3 + x^2 + (-2*a-2)*x + (-16*a-12) over Number Field in a with defining polynomial x^2 - x - 1 a_ps match
current prime =  79
singular curve
Elliptic Curve defined by y^2 + (a+1)*x*y = x^3 + x^2 + (-2*a-2)*x + (-16*a-12) over Number Field in a with defining polynomial x^2 - x - 1 tentative
Elliptic Curve defined by y^2 + (a+1)*x*y = x^3 + x^2 + (-2*a-2)*x + (-16*a-12) over Number Field in a with defining polynomial x^2 - x - 1 a_ps match
singular curve
Elliptic Curve defined by y^2 + (a+1)*x*y = x^3 + x^2 + (-2*a-2)*x + (-16*a-12) over Number Field in a with defining polynomial x^2 - x - 1 tentative
Elliptic Curve defined by y^2 + (a+1)*x*y = x^3 + x^2 + (-2*a-2)*x + (-16*a-12) over Number Field in a with defining polynomial x^2 - x - 1 a_ps match
current prime =  89
Elliptic Curve defined by y^2 + (a+1)*x*y = x^3 + x^2 + (-2*a-2)*x + (-16*a-12) over Number Field in a with defining polynomial x^2 - x - 1 tentative
Elliptic Curve defined by y^2 + (a+1)*x*y = x^3 + x^2 + (-2*a-2)*x + (-16*a-12) over Number Field in a with defining polynomial x^2 - x - 1 a_ps match
Elliptic Curve defined by y^2 + (a+1)*x*y = x^3 + x^2 + (-2*a-2)*x + (-16*a-12) over Number Field in a with defining polynomial x^2 - x - 1 tentative
Elliptic Curve defined by y^2 + (a+1)*x*y = x^3 + x^2 + (-2*a-2)*x + (-16*a-12) over Number Field in a with defining polynomial x^2 - x - 1 a_ps match

Fractional ideal (22)
7

current prime =  11
current prime =  19
singular curve
singular curve
Elliptic Curve defined by y^2 + x*y + (a+1)*y = x^3 + (-a)*x^2 + (-5*a-3)*x over Number Field in a with defining polynomial x^2 - x - 1 tentative
singular curve
singular curve
singular curve
singular curve
singular curve
current prime =  29
Elliptic Curve defined by y^2 + (a+1)*x*y + y = x^3 + (a+1)*x^2 + (5*a-17)*x + (-5*a-29) over Number Field in a with defining polynomial x^2 - x - 1 tentative
singular curve
singular curve
Elliptic Curve defined by y^2 + (a+1)*x*y + y = x^3 + (a+1)*x^2 + (10*a-12)*x + (15*a-23) over Number Field in a with defining polynomial x^2 - x - 1 tentative
singular curve
current prime =  31
Elliptic Curve defined by y^2 + (a+1)*x*y + y = x^3 + (a+1)*x^2 + (5*a-17)*x + (-5*a-29) over Number Field in a with defining polynomial x^2 - x - 1 tentative
singular curve
singular curve
Elliptic Curve defined by y^2 + (a+1)*x*y + y = x^3 + (a+1)*x^2 + (10*a-12)*x + (15*a-23) over Number Field in a with defining polynomial x^2 - x - 1 tentative
singular curve
singular curve
Elliptic Curve defined by y^2 + (a+1)*x*y + (a+1)*y = x^3 + (-a+1)*x^2 + (-21*a-7)*x + (-21*a-2) over Number Field in a with defining polynomial x^2 - x - 1 tentative
singular curve
singular curve
Elliptic Curve defined by y^2 + (a+1)*x*y + a*y = x^3 + (a+1)*x^2 + (-4*a-4)*x + (a+1) over Number Field in a with defining polynomial x^2 - x - 1 tentative
singular curve
Elliptic Curve defined by y^2 + (a+1)*x*y + a*y = x^3 + (a+1)*x^2 + (a+1)*x over Number Field in a with defining polynomial x^2 - x - 1 tentative
singular curve
Elliptic Curve defined by y^2 = x^3 + a*x^2 + (-12*a-4)*x + (-12*a-4) over Number Field in a with defining polynomial x^2 - x - 1 tentative
singular curve
current prime =  41
singular curve
Elliptic Curve defined by y^2 + x*y = x^3 + (-a)*x^2 + (-a-3)*x + (-a-3) over Number Field in a with defining polynomial x^2 - x - 1 tentative
singular curve
singular curve
singular curve
singular curve
Elliptic Curve defined by y^2 + (a+1)*x*y + y = x^3 + (a+1)*x^2 + (10*a-12)*x + (15*a-23) over Number Field in a with defining polynomial x^2 - x - 1 tentative
singular curve
Elliptic Curve defined by y^2 + x*y + (a+1)*y = x^3 + (-a)*x^2 + (-5*a-3)*x over Number Field in a with defining polynomial x^2 - x - 1 tentative
singular curve
Elliptic Curve defined by y^2 + (a+1)*x*y + y = x^3 + (a+1)*x^2 + (5*a-17)*x + (-5*a-29) over Number Field in a with defining polynomial x^2 - x - 1 tentative
singular curve
current prime =  59
Elliptic Curve defined by y^2 + (a+1)*x*y + y = x^3 + (a+1)*x^2 + (10*a-12)*x + (15*a-23) over Number Field in a with defining polynomial x^2 - x - 1 tentative
singular curve
Elliptic Curve defined by y^2 + (a+1)*x*y + y = x^3 + (a+1)*x^2 + (5*a-17)*x + (-5*a-29) over Number Field in a with defining polynomial x^2 - x - 1 tentative
singular curve
singular curve
singular curve
singular curve
singular curve
current prime =  61
Elliptic Curve defined by y^2 + (a+1)*x*y + y = x^3 + (a+1)*x^2 + (10*a-12)*x + (15*a-23) over Number Field in a with defining polynomial x^2 - x - 1 tentative
singular curve
singular curve
Elliptic Curve defined by y^2 + (a+1)*x*y + y = x^3 + (a+1)*x^2 + (5*a-17)*x + (-5*a-29) over Number Field in a with defining polynomial x^2 - x - 1 tentative
singular curve
singular curve
singular curve
singular curve
current prime =  71
singular curve
singular curve
singular curve
Elliptic Curve defined by y^2 + (a+1)*x*y + y = x^3 + (a+1)*x^2 + (10*a-12)*x + (15*a-23) over Number Field in a with defining polynomial x^2 - x - 1 tentative
singular curve
Elliptic Curve defined by y^2 + a*x*y + (a+1)*y = x^3 + (a-1)*x^2 + (-17*a-10)*x + (-63*a-39) over Number Field in a with defining polynomial x^2 - x - 1 tentative
singular curve
singular curve
Elliptic Curve defined by y^2 + (a+1)*x*y + y = x^3 + (a+1)*x^2 + (5*a-17)*x + (-5*a-29) over Number Field in a with defining polynomial x^2 - x - 1 tentative
singular curve
singular curve
current prime =  79
Elliptic Curve defined by y^2 + (a+1)*x*y + y = x^3 + (a+1)*x^2 + (5*a-17)*x + (-5*a-29) over Number Field in a with defining polynomial x^2 - x - 1 tentative
singular curve
Elliptic Curve defined by y^2 + a*x*y + (a+1)*y = x^3 + (a-1)*x^2 + (-17*a-10)*x + (-63*a-39) over Number Field in a with defining polynomial x^2 - x - 1 tentative
singular curve
Elliptic Curve defined by y^2 + (a+1)*x*y + y = x^3 + (a+1)*x^2 + (10*a-12)*x + (15*a-23) over Number Field in a with defining polynomial x^2 - x - 1 tentative
singular curve
current prime =  89
singular curve
Elliptic Curve defined by y^2 + (a+1)*x*y + y = x^3 + (a+1)*x^2 + (10*a-12)*x + (15*a-23) over Number Field in a with defining polynomial x^2 - x - 1 tentative
singular curve
Elliptic Curve defined by y^2 + a*x*y + (a+1)*y = x^3 + (a-1)*x^2 + (-17*a-10)*x + (-63*a-39) over Number Field in a with defining polynomial x^2 - x - 1 tentative
singular curve
Elliptic Curve defined by y^2 + (a+1)*x*y + y = x^3 + (a+1)*x^2 + (5*a-17)*x + (-5*a-29) over Number Field in a with defining polynomial x^2 - x - 1 tentative
singular curve
singular curve

Fractional ideal (-3*a + 24) Fractional ideal (-3*a + 24) Fractional ideal (-3*a + 24) Fractional ideal (-3*a + 24) Fractional ideal (-3*a + 24) Fractional ideal (-3*a + 24) Fractional ideal (-3*a + 24) Fractional ideal (-3*a + 24) Fractional ideal (-3*a + 24)
-4 -8 -6 6 -6 2
4 0 -2 2 14 -10
4 0 -2 2 14 -10
-4 -8 -6 6 -6 2
4 0 -2 2 14 -10
-4 -8 -6 6 -6 2
-4 -8 -6 6 -6 2
-4 -8 -6 6 -6 2
4 0 -2 2 14 -10

current prime =  11
current prime =  19
current prime =  29
singular curve
singular curve
singular curve
singular curve
singular curve
singular curve
current prime =  31
singular curve
(0, -a - 1, 0, 9*a + 3, a - 8) tentative
(0, a, 1, -4*a - 2, 4*a + 2) tentative
current prime =  41
current prime =  59
current prime =  61
singular curve
current prime =  71
current prime =  79
singular curve
current prime =  89

Fractional ideal (a + 22) 4 -4 -6 6 -4 4
Fractional ideal (a + 22) -5 0 10 0 2 -8

current prime =  11
current prime =  19
Elliptic Curve defined by y^2 + (a+1)*x*y + (a+1)*y = x^3 + (-a+1)*x^2 + (-4*a-6)*x + (-2*a) over Number Field in a with defining polynomial x^2 - x - 1 tentative
singular curve
current prime =  29
Elliptic Curve defined by y^2 + (a+1)*x*y + (a+1)*y = x^3 + (-a+1)*x^2 + (-4*a-6)*x + (-2*a) over Number Field in a with defining polynomial x^2 - x - 1 tentative
singular curve
Elliptic Curve defined by y^2 + x*y + (a+1)*y = x^3 + (a+1)*x^2 + (-28*a-18)*x + (-13*a-8) over Number Field in a with defining polynomial x^2 - x - 1 tentative
singular curve
current prime =  31
Elliptic Curve defined by y^2 + x*y + (a+1)*y = x^3 + (a+1)*x^2 + (-28*a-18)*x + (-13*a-8) over Number Field in a with defining polynomial x^2 - x - 1 tentative
singular curve
singular curve
Elliptic Curve defined by y^2 + (a+1)*x*y + (a+1)*y = x^3 + (-a+1)*x^2 + (-4*a-6)*x + (-2*a) over Number Field in a with defining polynomial x^2 - x - 1 tentative
singular curve
Elliptic Curve defined by y^2 + x*y + (a+1)*y = x^3 + (a+1)*x^2 + (-28*a-18)*x + (-13*a-8) over Number Field in a with defining polynomial x^2 - x - 1 tentative
singular curve
singular curve
Elliptic Curve defined by y^2 + (a+1)*x*y + (a+1)*y = x^3 + (-a+1)*x^2 + (-4*a-6)*x + (-2*a) over Number Field in a with defining polynomial x^2 - x - 1 tentative
singular curve
current prime =  41
Elliptic Curve defined by y^2 + (a+1)*x*y + (a+1)*y = x^3 + (-a+1)*x^2 + (-4*a-6)*x + (-2*a) over Number Field in a with defining polynomial x^2 - x - 1 tentative
singular curve
Elliptic Curve defined by y^2 + x*y + (a+1)*y = x^3 + (a+1)*x^2 + (-28*a-18)*x + (-13*a-8) over Number Field in a with defining polynomial x^2 - x - 1 tentative
singular curve
current prime =  59
Elliptic Curve defined by y^2 + (a+1)*x*y + (a+1)*y = x^3 + (-a+1)*x^2 + (-4*a-6)*x + (-2*a) over Number Field in a with defining polynomial x^2 - x - 1 tentative
singular curve
Elliptic Curve defined by y^2 + x*y + (a+1)*y = x^3 + (a+1)*x^2 + (-28*a-18)*x + (-13*a-8) over Number Field in a with defining polynomial x^2 - x - 1 tentative
singular curve
current prime =  61
Elliptic Curve defined by y^2 + x*y + (a+1)*y = x^3 + (a+1)*x^2 + (-28*a-18)*x + (-13*a-8) over Number Field in a with defining polynomial x^2 - x - 1 tentative
singular curve
Elliptic Curve defined by y^2 + (a+1)*x*y + (a+1)*y = x^3 + (-a+1)*x^2 + (-4*a-6)*x + (-2*a) over Number Field in a with defining polynomial x^2 - x - 1 tentative
singular curve
current prime =  71
Elliptic Curve defined by y^2 + (a+1)*x*y + (a+1)*y = x^3 + (-a+1)*x^2 + (-4*a-6)*x + (-2*a) over Number Field in a with defining polynomial x^2 - x - 1 tentative
singular curve
Elliptic Curve defined by y^2 + x*y + (a+1)*y = x^3 + (a+1)*x^2 + (-28*a-18)*x + (-13*a-8) over Number Field in a with defining polynomial x^2 - x - 1 tentative
singular curve
current prime =  79
singular curve
Elliptic Curve defined by y^2 + (a+1)*x*y + (a+1)*y = x^3 + (-a+1)*x^2 + (-4*a-6)*x + (-2*a) over Number Field in a with defining polynomial x^2 - x - 1 tentative
singular curve
Elliptic Curve defined by y^2 + x*y + (a+1)*y = x^3 + (a+1)*x^2 + (-28*a-18)*x + (-13*a-8) over Number Field in a with defining polynomial x^2 - x - 1 tentative
singular curve
current prime =  89
Elliptic Curve defined by y^2 + x*y + (a+1)*y = x^3 + (a+1)*x^2 + (-28*a-18)*x + (-13*a-8) over Number Field in a with defining polynomial x^2 - x - 1 tentative
singular curve
Elliptic Curve defined by y^2 + (a+1)*x*y + (a+1)*y = x^3 + (-a+1)*x^2 + (-4*a-6)*x + (-2*a) over Number Field in a with defining polynomial x^2 - x - 1 tentative
singular curve
singular curve

Fractional ideal (21*a - 14) -3 -1 -1 -6 -3 -1 -4 -4 -4 5 8 11 -7 13 -14 4 -2 5 -10 -9 6
Fractional ideal (21*a - 14) -3 -1 -1 -6 -3 -1 -4 -4 -4 5 8 11 -7 13 -14 4 -2 5 -10 -9 6

current prime =  11
current prime =  19
current prime =  29
Elliptic Curve defined by y^2 + (a+1)*x*y + y = x^3 + a*x^2 + (a-11)*x + (-22*a+8) over Number Field in a with defining polynomial x^2 - x - 1 tentative
singular curve
Elliptic Curve defined by y^2 + (a+1)*x*y + y = x^3 + a*x^2 + (a-11)*x + (-22*a+8) over Number Field in a with defining polynomial x^2 - x - 1 tentative
singular curve
current prime =  31
Elliptic Curve defined by y^2 + (a+1)*x*y + y = x^3 + a*x^2 + (a-11)*x + (-22*a+8) over Number Field in a with defining polynomial x^2 - x - 1 tentative
current prime =  41
singular curve
Elliptic Curve defined by y^2 + (a+1)*x*y + y = x^3 + a*x^2 + (a-11)*x + (-22*a+8) over Number Field in a with defining polynomial x^2 - x - 1 tentative
current prime =  59
singular curve
Elliptic Curve defined by y^2 + (a+1)*x*y + y = x^3 + a*x^2 + (a-11)*x + (-22*a+8) over Number Field in a with defining polynomial x^2 - x - 1 tentative
singular curve
current prime =  61
Elliptic Curve defined by y^2 + (a+1)*x*y + y = x^3 + a*x^2 + (a-11)*x + (-22*a+8) over Number Field in a with defining polynomial x^2 - x - 1 tentative
current prime =  71
Elliptic Curve defined by y^2 + (a+1)*x*y + y = x^3 + a*x^2 + (a-11)*x + (-22*a+8) over Number Field in a with defining polynomial x^2 - x - 1 tentative
singular curve
singular curve
Elliptic Curve defined by y^2 + (a+1)*x*y + y = x^3 + a*x^2 + (a-11)*x + (-22*a+8) over Number Field in a with defining polynomial x^2 - x - 1 tentative
singular curve
singular curve
current prime =  79
singular curve
singular curve
Elliptic Curve defined by y^2 + (a+1)*x*y + y = x^3 + a*x^2 + (a-11)*x + (-22*a+8) over Number Field in a with defining polynomial x^2 - x - 1 tentative
singular curve
singular curve
Elliptic Curve defined by y^2 + (a+1)*x*y + y = x^3 + a*x^2 + (a-11)*x + (-22*a+8) over Number Field in a with defining polynomial x^2 - x - 1 tentative
current prime =  89
singular curve
Elliptic Curve defined by y^2 + (a+1)*x*y + y = x^3 + a*x^2 + (a-11)*x + (-22*a+8) over Number Field in a with defining polynomial x^2 - x - 1 tentative
singular curve

Fractional ideal (21*a - 7) -3 2 2 6 6 2 2 8 -10 8 -10 8 2 4 -14 -8 -8 -4 -4 12 0

current prime =  11
singular curve
singular curve
Elliptic Curve defined by y^2 + (a+1)*x*y + a*y = x^3 + (a+1)*x^2 + (-4*a-9)*x + (6*a-4) over Number Field in a with defining polynomial x^2 - x - 1 tentative
singular curve
current prime =  19
Elliptic Curve defined by y^2 + (a+1)*x*y + a*y = x^3 + (a+1)*x^2 + (-4*a-9)*x + (6*a-4) over Number Field in a with defining polynomial x^2 - x - 1 tentative
current prime =  29
Elliptic Curve defined by y^2 + (a+1)*x*y + a*y = x^3 + (a+1)*x^2 + (-4*a-9)*x + (6*a-4) over Number Field in a with defining polynomial x^2 - x - 1 tentative
singular curve
Elliptic Curve defined by y^2 + (a+1)*x*y + a*y = x^3 + (a+1)*x^2 + (-4*a-9)*x + (6*a-4) over Number Field in a with defining polynomial x^2 - x - 1 tentative
singular curve
current prime =  31
Elliptic Curve defined by y^2 + (a+1)*x*y + a*y = x^3 + (a+1)*x^2 + (-4*a-9)*x + (6*a-4) over Number Field in a with defining polynomial x^2 - x - 1 tentative
singular curve
singular curve
current prime =  41
Elliptic Curve defined by y^2 + (a+1)*x*y + a*y = x^3 + (a+1)*x^2 + (-4*a-9)*x + (6*a-4) over Number Field in a with defining polynomial x^2 - x - 1 tentative
singular curve
singular curve
current prime =  59
Elliptic Curve defined by y^2 + (a+1)*x*y + a*y = x^3 + (a+1)*x^2 + (-4*a-9)*x + (6*a-4) over Number Field in a with defining polynomial x^2 - x - 1 tentative
Elliptic Curve defined by y^2 = x^3 + (a+1)*x^2 + (9*a-37)*x + (23*a-12) over Number Field in a with defining polynomial x^2 - x - 1 tentative
singular curve
Elliptic Curve defined by y^2 + (a+1)*x*y = x^3 + (-1)*x^2 + (8*a-13)*x over Number Field in a with defining polynomial x^2 - x - 1 tentative
Elliptic Curve defined by y^2 + (a+1)*x*y = x^3 + (-1)*x^2 + (-32*a+52)*x + (31*a-50) over Number Field in a with defining polynomial x^2 - x - 1 tentative
Elliptic Curve defined by y^2 + x*y = x^3 + a*x^2 + (a-2)*x over Number Field in a with defining polynomial x^2 - x - 1 tentative
Elliptic Curve defined by y^2 + x*y = x^3 + a*x^2 + (-4*a+8)*x + (3*a-2) over Number Field in a with defining polynomial x^2 - x - 1 tentative
Elliptic Curve defined by y^2 + a*x*y + (a+1)*y = x^3 + (-a+1)*x^2 + (-a+2)*x + (18*a+12) over Number Field in a with defining polynomial x^2 - x - 1 tentative
Elliptic Curve defined by y^2 + a*x*y + (a+1)*y = x^3 + (-a+1)*x^2 + (-6*a-3)*x + (5*a+3) over Number Field in a with defining polynomial x^2 - x - 1 tentative
singular curve
singular curve
current prime =  61
singular curve
singular curve
singular curve
singular curve
Elliptic Curve defined by y^2 + (a+1)*x*y + a*y = x^3 + (a+1)*x^2 + (-4*a-9)*x + (6*a-4) over Number Field in a with defining polynomial x^2 - x - 1 tentative
singular curve
singular curve
singular curve
singular curve
singular curve
Elliptic Curve defined by y^2 + (a+1)*x*y + a*y = x^3 + (a+1)*x^2 + (-4*a-9)*x + (6*a-4) over Number Field in a with defining polynomial x^2 - x - 1 tentative
singular curve
current prime =  71
Elliptic Curve defined by y^2 + (a+1)*x*y + a*y = x^3 + (a+1)*x^2 + (-4*a-9)*x + (6*a-4) over Number Field in a with defining polynomial x^2 - x - 1 tentative
current prime =  79
Elliptic Curve defined by y^2 + (a+1)*x*y + a*y = x^3 + (a+1)*x^2 + (11*a+1)*x + (73*a+36) over Number Field in a with defining polynomial x^2 - x - 1 tentative
singular curve
singular curve
Elliptic Curve defined by y^2 + (a+1)*x*y + a*y = x^3 + (a+1)*x^2 + (-4*a-9)*x + (6*a-4) over Number Field in a with defining polynomial x^2 - x - 1 tentative
singular curve
current prime =  89
Elliptic Curve defined by y^2 + (a+1)*x*y + a*y = x^3 + (a+1)*x^2 + (-4*a-9)*x + (6*a-4) over Number Field in a with defining polynomial x^2 - x - 1 tentative
singular curve
Elliptic Curve defined by y^2 + (a+1)*x*y + a*y = x^3 + (a+1)*x^2 + (11*a+1)*x + (73*a+36) over Number Field in a with defining polynomial x^2 - x - 1 tentative

Fractional ideal (21*a - 8) -1 -2 -10 0 6 2 8 -6 -6 8 -4 6 6 6 0 -10 -10 -6 6 -10 8 -6 -6
Fractional ideal (21*a - 8) 1 2 2 0 2 6 0 2 2 -8 -4 2 -2 6 0 2 2 -2 -10 -14 -8 -6 2
Fractional ideal (21*a - 8) -1 -2 -10 0 6 2 8 -6 -6 8 -4 6 6 6 0 -10 -10 -6 6 -10 8 -6 -6
Fractional ideal (21*a - 8) 1 2 2 0 2 6 0 2 2 -8 -4 2 -2 6 0 2 2 -2 -10 -14 -8 -6 2
Fractional ideal (21*a - 8) -1 -2 -10 0 6 2 8 -6 -6 8 -4 6 6 6 0 -10 -10 -6 6 -10 8 -6 -6
Fractional ideal (21*a - 8) -1 -2 -10 0 6 2 8 -6 -6 8 -4 6 6 6 0 -10 -10 -6 6 -10 8 -6 -6
Fractional ideal (21*a - 8) -1 -2 -10 0 6 2 8 -6 -6 8 -4 6 6 6 0 -10 -10 -6 6 -10 8 -6 -6
Fractional ideal (21*a - 8)

current prime =  11
singular curve
singular curve
current prime =  19
singular curve
current prime =  29
singular curve
current prime =  31
current prime =  41
singular curve
singular curve
singular curve
singular curve
current prime =  59
current prime =  61
current prime =  71
singular curve
singular curve
current prime =  79
singular curve
current prime =  89
singular curve

current prime =  11
current prime =  19
singular curve
current prime =  29
current prime =  31
singular curve
current prime =  41
singular curve
current prime =  59
current prime =  61
singular curve
current prime =  71
singular curve
singular curve
current prime =  79
current prime =  89
singular curve

current prime =  11
singular curve
singular curve
singular curve
current prime =  19
singular curve
singular curve
singular curve
(a, 1, 0, -7*a - 5, -16*a - 11) tentative
singular curve
singular curve
current prime =  29
singular curve
(a, 1, 0, -7*a - 5, -16*a - 11) tentative
current prime =  31
(a, 1, 0, -7*a - 5, -16*a - 11) tentative
current prime =  41
(a, 1, 0, -7*a - 5, -16*a - 11) tentative
current prime =  59
(a, 1, 0, -7*a - 5, -16*a - 11) tentative
current prime =  61
(a, 1, 0, -7*a - 5, -16*a - 11) tentative
singular curve
current prime =  71
(a, 1, 0, -7*a - 5, -16*a - 11) tentative
current prime =  79
(a, 1, 0, -7*a - 5, -16*a - 11) tentative
current prime =  89
(a, 1, 0, -7*a - 5, -16*a - 11) tentative

Fractional ideal (a - 25) -1 2 2 11 -3 5 2 0 2 1 -3 -1 6 -5 -12 3 1 -12 -2 7 11 5 -2 -15

current prime =  11
current prime =  19
(a + 1, -1, 1, 5*a - 12, 7*a - 14) tentative
(1, 0, 1, a - 2, -2*a + 3) tentative
singular curve
current prime =  29
(a + 1, -1, 1, 5*a - 12, 7*a - 14) tentative
current prime =  31
current prime =  41
(a + 1, -1, 1, 5*a - 12, 7*a - 14) tentative
current prime =  59
singular curve
(a + 1, -1, 1, 5*a - 12, 7*a - 14) tentative
singular curve
singular curve
singular curve
current prime =  61
singular curve
singular curve
(a + 1, -1, 1, 5*a - 12, 7*a - 14) tentative
singular curve
singular curve
current prime =  71
(a + 1, -1, 1, 5*a - 12, 7*a - 14) tentative
current prime =  79
(a + 1, -1, 1, 5*a - 12, 7*a - 14) tentative
singular curve
current prime =  89
singular curve
(a + 1, -1, 1, 5*a - 12, 7*a - 14) tentative
singular curve

Fractional ideal (2*a - 26) 4 -9 1 -3 6 5 -2 7 8 -4 6 3 -5 -14 14 -5 -14 10 10 -9
Fractional ideal (2*a - 26) 4 5 -3 3 2 -7 6 9 -12 0 -6 -3 -1 -10 -6 9 -10 -10 -6 15

current prime =  11
singular curve
current prime =  19
current prime =  29
singular curve
current prime =  31
current prime =  41
singular curve
current prime =  59
current prime =  61
current prime =  71
current prime =  79
singular curve
singular curve
current prime =  89
singular curve
(a + 1, a, a, 13*a - 25, 30*a - 49) tentative

Fractional ideal (3*a + 24) [-1, '?', 4, -4, 0, 0, 6, 0, -6, 6, -2, 0, -10, 0, 4, -2, -12, -2, -2, '?', '?', -14, 16, -2, 10]

current prime =  11
singular curve
singular curve
singular curve
singular curve
singular curve
singular curve
singular curve
singular curve
singular curve
singular curve
singular curve
singular curve
singular curve
singular curve
current prime =  19
current prime =  29
singular curve
singular curve
singular curve
singular curve
singular curve
singular curve
current prime =  31
singular curve
singular curve
singular curve
current prime =  41
singular curve
singular curve
singular curve
current prime =  59
singular curve
(a + 1, a, a, 13*a - 25, 30*a - 49) tentative
current prime =  61
singular curve
(a + 1, a, a, 13*a - 25, 30*a - 49) tentative
current prime =  71
current prime =  79
singular curve
(a + 1, a, a, 13*a - 25, 30*a - 49) tentative
current prime =  89
(a + 1, a, a, 13*a - 25, 30*a - 49) tentative
singular curve

Fractional ideal (3*a + 24) [(-1, 2), ('?', 3), (4, 5), (-4, 7), (0, 11), (0, 11), (6, 19), (0, 19), (-6, 29), (6, 29), (-2, 31), (0, 31), (-10, 41), (0, 41), (4, 59), (-2, 59), (-12, 61), (-2, 61), (-2, 71), ('?', 71), ('?', 71), (-14, 79), (16, 79), (-2, 89), (10, 89)]

Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
  File "_sage_input_5.py", line 10, in <module>
    exec compile(u'open("___code___.py","w").write("# -*- coding: utf-8 -*-\\n" + _support_.preparse_worksheet_cell(base64.b64decode("RTI9RWxsaXB0aWNDdXJ2ZShLLFsxLCAtYSArIDEsIGEgKyAxLCAtMTEqYSAtIDYsIC0xOCphIC0gMTFdKQpFMi5jb25kdWN0b3IoKS5ub3JtKCk="),globals())+"\\n"); execfile(os.path.abspath("___code___.py"))
  File "", line 1, in <module>
    
  File "/private/var/folders/+3/+3+bRf7bGhaMk-2vvrWEvU+++TI/-Tmp-/tmpUXECyo/___code___.py", line 3, in <module>
    E2=EllipticCurve(K,[_sage_const_1 , -a + _sage_const_1 , a + _sage_const_1 , -_sage_const_11 *a - _sage_const_6 , -_sage_const_18 *a - _sage_const_11 ])
  File "/Applications/sage/local/lib/python2.6/site-packages/sage/schemes/elliptic_curves/constructor.py", line 281, in EllipticCurve
    return ell_number_field.EllipticCurve_number_field(x, y)
  File "/Applications/sage/local/lib/python2.6/site-packages/sage/schemes/elliptic_curves/ell_number_field.py", line 163, in __init__
    EllipticCurve_field.__init__(self, [field(x) for x in ainvs])
  File "/Applications/sage/local/lib/python2.6/site-packages/sage/schemes/elliptic_curves/ell_generic.py", line 164, in __init__
    "Invariants %s define a singular curve."%ainvs
ArithmeticError: Invariants [1, -a + 1, a + 1, -11*a - 6, -18*a - 11] define a singular curve.

WARNING: Output truncated!  
full_output.txt



(1L, 'of', 392L, '---', 29L)
(2L, 'of', 392L, '---', 29L)
(3L, 'of', 392L, '---', 29L)
(4L, 'of', 392L, '---', 29L)
(5L, 'of', 392L, '---', 29L)
(6L, 'of', 392L, '---', 29L)
(7L, 'of', 392L, '---', 29L)
(8L, 'of', 392L, '---', 29L)
(9L, 'of', 392L, '---', 29L)
(10L, 'of', 392L, '---', 29L)
(11L, 'of', 392L, '---', 29L)
(12L, 'of', 392L, '---', 29L)
(13L, 'of', 392L, '---', 29L)
(14L, 'of', 392L, '---', 29L)
(15L, 'of', 392L, '---', 29L)
(16L, 'of', 392L, '---', 29L)
(17L, 'of', 392L, '---', 29L)
(18L, 'of', 392L, '---', 29L)
(19L, 'of', 392L, '---', 29L)
(20L, 'of', 392L, '---', 29L)
(21L, 'of', 392L, '---', 29L)
(22L, 'of', 392L, '---', 29L)
(23L, 'of', 392L, '---', 29L)
(24L, 'of', 392L, '---', 29L)
(25L, 'of', 392L, '---', 29L)
(26L, 'of', 392L, '---', 29L)
(27L, 'of', 392L, '---', 29L)
(28L, 'of', 392L, '---', 29L)
(29L, 'of', 392L, '---', 29L)
(30L, 'of', 392L, '---', 29L)
(31L, 'of', 392L, '---', 29L)
(32L, 'of', 392L, '---', 29L)
(33L, 'of', 392L, '---', 29L)
(34L, 'of', 392L, '---', 29L)
(35L, 'of', 392L, '---', 29L)
(36L, 'of', 392L, '---', 29L)
(37L, 'of', 392L, '---', 29L)
(38L, 'of', 392L, '---', 29L)
(39L, 'of', 392L, '---', 29L)
(40L, 'of', 392L, '---', 29L)
(41L, 'of', 392L, '---', 29L)
(42L, 'of', 392L, '---', 29L)
(43L, 'of', 392L, '---', 29L)
(44L, 'of', 392L, '---', 29L)
(45L, 'of', 392L, '---', 29L)
(46L, 'of', 392L, '---', 29L)
(47L, 'of', 392L, '---', 29L)
(48L, 'of', 392L, '---', 29L)
(49L, 'of', 392L, '---', 29L)
(50L, 'of', 392L, '---', 29L)
(51L, 'of', 392L, '---', 29L)
(52L, 'of', 392L, '---', 29L)
(53L, 'of', 392L, '---', 29L)
(54L, 'of', 392L, '---', 29L)
(55L, 'of', 392L, '---', 29L)
(56L, 'of', 392L, '---', 29L)
(57L, 'of', 392L, '---', 29L)
(58L, 'of', 392L, '---', 29L)
(59L, 'of', 392L, '---', 29L)

...

(333L, 'of', 392L, '---', 29L)
(334L, 'of', 392L, '---', 29L)
(335L, 'of', 392L, '---', 29L)
(336L, 'of', 392L, '---', 29L)
(337L, 'of', 392L, '---', 29L)
(338L, 'of', 392L, '---', 29L)
(339L, 'of', 392L, '---', 29L)
(340L, 'of', 392L, '---', 29L)
(341L, 'of', 392L, '---', 29L)
(342L, 'of', 392L, '---', 29L)
(343L, 'of', 392L, '---', 29L)
(344L, 'of', 392L, '---', 29L)
(345L, 'of', 392L, '---', 29L)
(346L, 'of', 392L, '---', 29L)
(347L, 'of', 392L, '---', 29L)
(348L, 'of', 392L, '---', 29L)
(349L, 'of', 392L, '---', 29L)
(350L, 'of', 392L, '---', 29L)
(351L, 'of', 392L, '---', 29L)
(352L, 'of', 392L, '---', 29L)
(353L, 'of', 392L, '---', 29L)
(354L, 'of', 392L, '---', 29L)
(355L, 'of', 392L, '---', 29L)
(356L, 'of', 392L, '---', 29L)
(357L, 'of', 392L, '---', 29L)
(358L, 'of', 392L, '---', 29L)
(359L, 'of', 392L, '---', 29L)
(360L, 'of', 392L, '---', 29L)
(361L, 'of', 392L, '---', 29L)
(362L, 'of', 392L, '---', 29L)
(363L, 'of', 392L, '---', 29L)
(364L, 'of', 392L, '---', 29L)
(365L, 'of', 392L, '---', 29L)
(366L, 'of', 392L, '---', 29L)
(367L, 'of', 392L, '---', 29L)
(368L, 'of', 392L, '---', 29L)
(369L, 'of', 392L, '---', 29L)
(370L, 'of', 392L, '---', 29L)
(371L, 'of', 392L, '---', 29L)
(372L, 'of', 392L, '---', 29L)
(373L, 'of', 392L, '---', 29L)
(374L, 'of', 392L, '---', 29L)
(375L, 'of', 392L, '---', 29L)
(376L, 'of', 392L, '---', 29L)
(377L, 'of', 392L, '---', 29L)
(378L, 'of', 392L, '---', 29L)
(379L, 'of', 392L, '---', 29L)
(380L, 'of', 392L, '---', 29L)
(381L, 'of', 392L, '---', 29L)
(382L, 'of', 392L, '---', 29L)
(383L, 'of', 392L, '---', 29L)
(384L, 'of', 392L, '---', 29L)
(385L, 'of', 392L, '---', 29L)
(386L, 'of', 392L, '---', 29L)
(387L, 'of', 392L, '---', 29L)
(388L, 'of', 392L, '---', 29L)
(389L, 'of', 392L, '---', 29L)
(390L, 'of', 392L, '---', 29L)
(391L, 'of', 392L, '---', 29L)
(392L, 'of', 392L, '---', 29L)

False

True

(19*a, -57*a - 76, 38*a + 19, 156*a + 93, 4919*a + 3019)

12

11

5 loops, best of 3: 41.1 ms per loop

WARNING: Output truncated!  
full_output.txt



0 0 0 0 0 0 17 4 17 17
0 0 0 0 0 0 17 4 -2 17
0 0 0 0 0 0 17 4 -2 -2
0 0 0 0 0 0 17 4 17 -2
0 0 0 0 0 0 -2 4 17 17
0 0 0 0 0 0 -2 4 -2 17
0 0 0 0 0 0 -2 4 -2 -2
0 0 0 0 0 0 -2 4 17 -2
0 0 0 0 0 0 -2 -15 17 17
0 0 0 0 0 0 -2 -15 -2 17
0 0 0 0 0 0 -2 -15 -2 -2
0 0 0 0 0 0 -2 -15 17 -2
0 0 0 0 0 0 17 -15 17 17
0 0 0 0 0 0 17 -15 -2 17
0 0 0 0 0 0 17 -15 -2 -2
0 0 0 0 0 0 17 -15 17 -2
0 0 0 0 1 0 17 4 12 17
0 0 0 0 1 0 17 4 -7 17
0 0 0 0 1 0 17 4 -7 -2
0 0 0 0 1 0 17 4 12 -2
0 0 0 0 1 0 -2 4 12 17
0 0 0 0 1 0 -2 4 -7 17
0 0 0 0 1 0 -2 4 -7 -2
0 0 0 0 1 0 -2 4 12 -2
0 0 0 0 1 0 -2 -15 12 17
0 0 0 0 1 0 -2 -15 -7 17
0 0 0 0 1 0 -2 -15 -7 -2
0 0 0 0 1 0 -2 -15 12 -2
0 0 0 0 1 0 17 -15 12 17
0 0 0 0 1 0 17 -15 -7 17
0 0 0 0 1 0 17 -15 -7 -2
0 0 0 0 1 0 17 -15 12 -2
0 0 0 0 1 1 17 4 7 2
0 0 0 0 1 1 17 4 -12 2
0 0 0 0 1 1 17 4 -12 -17
0 0 0 0 1 1 17 4 7 -17
0 0 0 0 1 1 -2 4 7 2
0 0 0 0 1 1 -2 4 -12 2
0 0 0 0 1 1 -2 4 -12 -17
0 0 0 0 1 1 -2 4 7 -17
0 0 0 0 1 1 -2 -15 7 2
0 0 0 0 1 1 -2 -15 -12 2
0 0 0 0 1 1 -2 -15 -12 -17
0 0 0 0 1 1 -2 -15 7 -17
0 0 0 0 1 1 17 -15 7 2
0 0 0 0 1 1 17 -15 -12 2
0 0 0 0 1 1 17 -15 -12 -17
0 0 0 0 1 1 17 -15 7 -17
0 0 0 0 0 1 17 4 12 12
0 0 0 0 0 1 17 4 -7 12
0 0 0 0 0 1 17 4 -7 -7
0 0 0 0 0 1 17 4 12 -7
0 0 0 0 0 1 -2 4 12 12
0 0 0 0 0 1 -2 4 -7 12
0 0 0 0 0 1 -2 4 -7 -7
0 0 0 0 0 1 -2 4 12 -7
0 0 0 0 0 1 -2 -15 12 12
0 0 0 0 0 1 -2 -15 -7 12
0 0 0 0 0 1 -2 -15 -7 -7

...

0 1 -1 -1 1 0 5 10 -15 13
0 1 -1 -1 1 0 5 10 -15 -6
0 1 -1 -1 1 0 5 10 4 -6
0 1 -1 -1 1 0 -14 10 4 13
0 1 -1 -1 1 0 -14 10 -15 13
0 1 -1 -1 1 0 -14 10 -15 -6
0 1 -1 -1 1 0 -14 10 4 -6
0 1 -1 -1 1 0 -14 -9 4 13
0 1 -1 -1 1 0 -14 -9 -15 13
0 1 -1 -1 1 0 -14 -9 -15 -6
0 1 -1 -1 1 0 -14 -9 4 -6
0 1 -1 -1 1 0 5 -9 4 13
0 1 -1 -1 1 0 5 -9 -15 13
0 1 -1 -1 1 0 5 -9 -15 -6
0 1 -1 -1 1 0 5 -9 4 -6
0 1 -1 -1 1 1 5 0 18 17
0 1 -1 -1 1 1 5 0 -1 17
0 1 -1 -1 1 1 5 0 -1 -2
0 1 -1 -1 1 1 5 0 18 -2
0 1 -1 -1 1 1 -14 0 18 17
0 1 -1 -1 1 1 -14 0 -1 17
0 1 -1 -1 1 1 -14 0 -1 -2
0 1 -1 -1 1 1 -14 0 18 -2
0 1 -1 -1 1 1 -14 -19 18 17
0 1 -1 -1 1 1 -14 -19 -1 17
0 1 -1 -1 1 1 -14 -19 -1 -2
0 1 -1 -1 1 1 -14 -19 18 -2
0 1 -1 -1 1 1 5 -19 18 17
0 1 -1 -1 1 1 5 -19 -1 17
0 1 -1 -1 1 1 5 -19 -1 -2
0 1 -1 -1 1 1 5 -19 18 -2
0 1 -1 -1 0 1 15 10 4 8
0 1 -1 -1 0 1 15 10 -15 8
0 1 -1 -1 0 1 15 10 -15 -11
0 1 -1 -1 0 1 15 10 4 -11
0 1 -1 -1 0 1 -4 10 4 8
0 1 -1 -1 0 1 -4 10 -15 8
0 1 -1 -1 0 1 -4 10 -15 -11
0 1 -1 -1 0 1 -4 10 4 -11
0 1 -1 -1 0 1 -4 -9 4 8
0 1 -1 -1 0 1 -4 -9 -15 8
0 1 -1 -1 0 1 -4 -9 -15 -11
0 1 -1 -1 0 1 -4 -9 4 -11
0 1 -1 -1 0 1 15 -9 4 8
0 1 -1 -1 0 1 15 -9 -15 8
0 1 -1 -1 0 1 15 -9 -15 -11
0 1 -1 -1 0 1 15 -9 4 -11
0 1 -1 0 0 0 18 13 18 12
0 1 -1 0 0 0 18 13 -1 12
0 1 -1 0 0 0 18 13 -1 -7
0 1 -1 0 0 0 18 13 18 -7
0 1 -1 0 0 0 -1 13 18 12
0 1 -1 0 0 0 -1 13 -1 12
0 1 -1 0 0 0 -1 13 -1 -7
0 1 -1 0 0 0 -1 13 18 -7
0 1 -1 0 0 0 -1 -6 18 12
0 1 -1 0 0 0 -1 -6 -1 12
0 1 -1 0 0 0 -1 -6 -1 -7
Elliptic Curve defined by y^2 + a*x*y = x^3 + (-1)*x^2 + (-6*a-1)*x + (-7*a-1) over Number Field in a with defining polynomial x^2 - x - 1 tentative
Elliptic Curve defined by y^2 + a*x*y = x^3 + (-1)*x^2 + (-6*a-1)*x + (-7*a-1) over Number Field in a with defining polynomial x^2 - x - 1 a_ps match

5

Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
  File "_sage_input_81.py", line 10, in <module>
    exec compile(u'open("___code___.py","w").write("# -*- coding: utf-8 -*-\\n" + _support_.preparse_worksheet_cell(base64.b64decode("bGVuKEUucG9pbnRzKCkp"),globals())+"\\n"); execfile(os.path.abspath("___code___.py"))
  File "", line 1, in <module>
    
  File "/private/var/folders/+3/+3+bRf7bGhaMk-2vvrWEvU+++TI/-Tmp-/tmpCVW6kQ/___code___.py", line 2, in <module>
    exec compile(u'len(E.points())
  File "", line 1, in <module>
    
  File "parent.pyx", line 705, in sage.structure.parent.Parent.__getattr__ (sage/structure/parent.c:5410)
  File "parent.pyx", line 172, in sage.structure.parent.raise_attribute_error (sage/structure/parent.c:2638)
AttributeError: 'EllipticCurve_number_field' object has no attribute 'points'

<type 'long'>
0
0
(0L, 0L, 201581136L)

14

(0L, 0L, 201581008L)

-1221

4294967296

python(24680) malloc: *** error for object 0x10c211f80: pointer being freed was not allocated
*** set a breakpoint in malloc_error_break to debug

Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
  File "_sage_input_2.py", line 10, in <module>
    exec compile(u'open("___code___.py","w").write("# -*- coding: utf-8 -*-\\n" + _support_.preparse_worksheet_cell(base64.b64decode("RQ=="),globals())+"\\n"); execfile(os.path.abspath("___code___.py"))
  File "", line 1, in <module>
    
  File "/private/var/folders/+3/+3+bRf7bGhaMk-2vvrWEvU+++TI/-Tmp-/tmpOwPB72/___code___.py", line 2, in <module>
    exec compile(u'E
  File "", line 1, in <module>
    
NameError: name 'E' is not defined

2346173225

Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
  File "_sage_input_6.py", line 10, in <module>
    exec compile(u'open("___code___.py","w").write("# -*- coding: utf-8 -*-\\n" + _support_.preparse_worksheet_cell(base64.b64decode("cHJpbnQgbm9ybSgxMCs1MyphKSwgMTBeMisxMCo1My01M14y"),globals())+"\\n"); execfile(os.path.abspath("___code___.py"))
  File "", line 1, in <module>
    
  File "/private/var/folders/+3/+3+bRf7bGhaMk-2vvrWEvU+++TI/-Tmp-/tmpk75WuL/___code___.py", line 3, in <module>
    exec compile(u'print norm(_sage_const_10 +_sage_const_53 *a), _sage_const_10 **_sage_const_2 +_sage_const_10 *_sage_const_53 -_sage_const_53 **_sage_const_2 
  File "", line 1, in <module>
    
NameError: name 'a' is not defined

640960480080

18446744073709551616

7880599

23068249636L

24*a + 17
52*a + 35
184*a + 153
1218*a + 772
-189172
-241774
-241774*a - 189172
23068249636

23068249636

4294967296

625 loops, best of 3: 20.6 µs per loop

625 loops, best of 3: 281 µs per loop

125 loops, best of 3: 2.61 ms per loop

810*a + 504

46959616

26

0
1
4
9
16
25
36
49
64
81
100
121
144
169
196
225
256
289
324
361
400
441
484
529
576
625
676
729
784
841
900
961
1024
1089
1156
1225
1296
1369
1444
1521
1600
1681
1764
1849
1936
2025
2116
2209
2304
2401
2500
2601
2704
2809
2916
3025
3136
3249
3364
3481
3600
3721
3844
3969
4096
4225
4356
4489
4624
4761
4900
5041
5184
5329
5476
5625
5776
5929
6084
6241
6400
6561
6724
6889
7056
7225
7396
7569
7744
7921
8100
8281
8464
8649
8836
9025
9216
9409
9604
9801