Atkin-Lehner |
2+ 3+ 5+ 31- |
Signs for the Atkin-Lehner involutions |
Class |
74400i |
Isogeny class |
Conductor |
74400 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
deg |
294912 |
Modular degree for the optimal curve |
Δ |
3940700625000000 = 26 · 38 · 510 · 312 |
Discriminant |
Eigenvalues |
2+ 3+ 5+ 0 -4 -2 -2 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-41758,1304512] |
[a1,a2,a3,a4,a6] |
Generators |
[-213:700:1] [-137:2106:1] |
Generators of the group modulo torsion |
j |
8052916245184/3940700625 |
j-invariant |
L |
8.9543281338062 |
L(r)(E,1)/r! |
Ω |
0.39130053271089 |
Real period |
R |
11.441753058456 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999611 |
(Analytic) order of Ш |
t |
4 |
Number of elements in the torsion subgroup |
Twists |
74400y1 14880r1 |
Quadratic twists by: -4 5 |