Atkin-Lehner |
2+ 5+ 13- 23- |
Signs for the Atkin-Lehner involutions |
Class |
68770c |
Isogeny class |
Conductor |
68770 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
304128 |
Modular degree for the optimal curve |
Δ |
22131365405500 = 22 · 53 · 13 · 237 |
Discriminant |
Eigenvalues |
2+ 1 5+ 1 0 13- 3 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,1,-146809,-21661904] |
[a1,a2,a3,a4,a6] |
Generators |
[665:12892:1] |
Generators of the group modulo torsion |
j |
2363798675161/149500 |
j-invariant |
L |
4.9192071434325 |
L(r)(E,1)/r! |
Ω |
0.24390089110697 |
Real period |
R |
2.5211096608056 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000001304 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
2990d1 |
Quadratic twists by: -23 |