Atkin-Lehner |
2- 3- 31- |
Signs for the Atkin-Lehner involutions |
Class |
69192bj |
Isogeny class |
Conductor |
69192 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
921600 |
Modular degree for the optimal curve |
Δ |
8664492536749008 = 24 · 39 · 317 |
Discriminant |
Eigenvalues |
2- 3- 2 0 4 2 6 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-2415954,-1445369947] |
[a1,a2,a3,a4,a6] |
j |
150651000832/837 |
j-invariant |
L |
4.3594332908424 |
L(r)(E,1)/r! |
Ω |
0.12109536879946 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
9 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
23064b1 2232k1 |
Quadratic twists by: -3 -31 |