Atkin-Lehner |
2- 3- 13+ 47+ |
Signs for the Atkin-Lehner involutions |
Class |
117312cq |
Isogeny class |
Conductor |
117312 |
Conductor |
∏ cp |
36 |
Product of Tamagawa factors cp |
deg |
681984 |
Modular degree for the optimal curve |
Δ |
1038841768306368 = 26 · 39 · 132 · 474 |
Discriminant |
Eigenvalues |
2- 3- 4 -2 0 13+ 2 -6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-35816,-2110038] |
[a1,a2,a3,a4,a6] |
Generators |
[1153:38610:1] |
Generators of the group modulo torsion |
j |
79393894876150336/16231902629787 |
j-invariant |
L |
11.589476556648 |
L(r)(E,1)/r! |
Ω |
0.35202381005636 |
Real period |
R |
3.65804693829 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999753321 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
117312bz1 58656q2 |
Quadratic twists by: -4 8 |