Atkin-Lehner |
2- 7- 13- 29+ |
Signs for the Atkin-Lehner involutions |
Class |
68614ba |
Isogeny class |
Conductor |
68614 |
Conductor |
∏ cp |
84 |
Product of Tamagawa factors cp |
deg |
245952 |
Modular degree for the optimal curve |
Δ |
-81120411008 = -1 · 27 · 73 · 133 · 292 |
Discriminant |
Eigenvalues |
2- -3 0 7- -3 13- -6 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-15255,729135] |
[a1,a2,a3,a4,a6] |
Generators |
[85:-246:1] [-55:1210:1] |
Generators of the group modulo torsion |
j |
-178691379328125/36923264 |
j-invariant |
L |
9.7172963044041 |
L(r)(E,1)/r! |
Ω |
1.0523789346331 |
Real period |
R |
0.1099243770993 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999983 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
68614e1 |
Quadratic twists by: 13 |