Atkin-Lehner |
2- 31- 61+ |
Signs for the Atkin-Lehner involutions |
Class |
117242k |
Isogeny class |
Conductor |
117242 |
Conductor |
∏ cp |
48 |
Product of Tamagawa factors cp |
deg |
322560 |
Modular degree for the optimal curve |
Δ |
59993327927296 = 224 · 312 · 612 |
Discriminant |
Eigenvalues |
2- -1 3 -1 3 1 3 5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,1,-20294,-1056957] |
[a1,a2,a3,a4,a6] |
Generators |
[-87:287:1] |
Generators of the group modulo torsion |
j |
961843977602977/62428020736 |
j-invariant |
L |
12.030737000619 |
L(r)(E,1)/r! |
Ω |
0.4016270060084 |
Real period |
R |
0.62406249907982 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000044367 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
117242g1 |
Quadratic twists by: -31 |