Atkin-Lehner |
2- 3- 5+ 17+ 31+ |
Signs for the Atkin-Lehner involutions |
Class |
31620i |
Isogeny class |
Conductor |
31620 |
Conductor |
∏ cp |
22 |
Product of Tamagawa factors cp |
deg |
133056 |
Modular degree for the optimal curve |
Δ |
-222494605438320 = -1 · 24 · 311 · 5 · 17 · 314 |
Discriminant |
Eigenvalues |
2- 3- 5+ -1 1 4 17+ -7 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-57466,-5369851] |
[a1,a2,a3,a4,a6] |
Generators |
[3797:233523:1] |
Generators of the group modulo torsion |
j |
-1311729218364722944/13905912839895 |
j-invariant |
L |
6.263215172628 |
L(r)(E,1)/r! |
Ω |
0.15407840698145 |
Real period |
R |
1.8477060110706 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
126480x1 94860p1 |
Quadratic twists by: -4 -3 |