Atkin-Lehner |
2- 3- 5+ 13+ |
Signs for the Atkin-Lehner involutions |
Class |
37440du |
Isogeny class |
Conductor |
37440 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
1720320 |
Modular degree for the optimal curve |
Δ |
140109105240000 = 26 · 313 · 54 · 133 |
Discriminant |
Eigenvalues |
2- 3- 5+ 0 -4 13+ 2 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-57658143,-168515203808] |
[a1,a2,a3,a4,a6] |
Generators |
[11722490026191929754463834:330544238019817653984459825:1283824656646370800424] |
Generators of the group modulo torsion |
j |
454357982636417669333824/3003024375 |
j-invariant |
L |
4.2960538144162 |
L(r)(E,1)/r! |
Ω |
0.05478786688982 |
Real period |
R |
39.206251842726 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
37440dr1 18720bo2 12480cu1 |
Quadratic twists by: -4 8 -3 |