Atkin-Lehner |
2+ 3+ 37- 47- |
Signs for the Atkin-Lehner involutions |
Class |
31302a |
Isogeny class |
Conductor |
31302 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
144000 |
Modular degree for the optimal curve |
Δ |
67401057042432 = 220 · 33 · 373 · 47 |
Discriminant |
Eigenvalues |
2+ 3+ 0 0 4 2 2 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-149817,22353773] |
[a1,a2,a3,a4,a6] |
Generators |
[373:4087:1] |
Generators of the group modulo torsion |
j |
13773517575474796875/2496335446016 |
j-invariant |
L |
4.7225907745507 |
L(r)(E,1)/r! |
Ω |
0.59953982798648 |
Real period |
R |
2.625675311909 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999999 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
31302j1 |
Quadratic twists by: -3 |