Atkin-Lehner |
2- 3+ 13- 23- |
Signs for the Atkin-Lehner involutions |
Class |
57408cq |
Isogeny class |
Conductor |
57408 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
110592 |
Modular degree for the optimal curve |
Δ |
3742433031168 = 210 · 312 · 13 · 232 |
Discriminant |
Eigenvalues |
2- 3+ 0 0 -4 13- 2 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-22373,-1277259] |
[a1,a2,a3,a4,a6] |
Generators |
[-83:32:1] [1300:46529:1] |
Generators of the group modulo torsion |
j |
1209527744512000/3654719757 |
j-invariant |
L |
8.6171850499103 |
L(r)(E,1)/r! |
Ω |
0.39043232640427 |
Real period |
R |
11.03544003294 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999987 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
57408bn1 14352bb1 |
Quadratic twists by: -4 8 |