Atkin-Lehner |
2+ 3+ 5- 13+ 59+ |
Signs for the Atkin-Lehner involutions |
Class |
69030c |
Isogeny class |
Conductor |
69030 |
Conductor |
∏ cp |
6 |
Product of Tamagawa factors cp |
deg |
4928256 |
Modular degree for the optimal curve |
Δ |
2675304834269184000 = 223 · 39 · 53 · 133 · 59 |
Discriminant |
Eigenvalues |
2+ 3+ 5- -1 1 13+ -2 3 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-87042939,312592572773] |
[a1,a2,a3,a4,a6] |
j |
3705382636318975619061027/135919566848000 |
j-invariant |
L |
1.1341451355625 |
L(r)(E,1)/r! |
Ω |
0.18902418613313 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
69030y1 |
Quadratic twists by: -3 |