Atkin-Lehner |
2+ 3- 13+ 23+ |
Signs for the Atkin-Lehner involutions |
Class |
57408x |
Isogeny class |
Conductor |
57408 |
Conductor |
∏ cp |
40 |
Product of Tamagawa factors cp |
deg |
768000 |
Modular degree for the optimal curve |
Δ |
6282617351765234688 = 210 · 310 · 135 · 234 |
Discriminant |
Eigenvalues |
2+ 3- 0 2 0 13+ -6 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-666453,170981019] |
[a1,a2,a3,a4,a6] |
j |
31969289829351424000/6135368507583237 |
j-invariant |
L |
2.2620575184826 |
L(r)(E,1)/r! |
Ω |
0.22620575173006 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
57408ce1 3588d1 |
Quadratic twists by: -4 8 |