Atkin-Lehner |
2+ 3- 5+ 7- 13+ |
Signs for the Atkin-Lehner involutions |
Class |
57330z |
Isogeny class |
Conductor |
57330 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
deg |
1843200 |
Modular degree for the optimal curve |
Δ |
8766258146755200000 = 210 · 39 · 55 · 77 · 132 |
Discriminant |
Eigenvalues |
2+ 3- 5+ 7- 2 13+ 6 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-5365215,-4779850419] |
[a1,a2,a3,a4,a6] |
Generators |
[-2913066:-1344699:2197] |
Generators of the group modulo torsion |
j |
199144987475642209/102211200000 |
j-invariant |
L |
4.7040230872908 |
L(r)(E,1)/r! |
Ω |
0.099201022089339 |
Real period |
R |
5.9273873747279 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000322 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
19110dc1 8190y1 |
Quadratic twists by: -3 -7 |