Atkin-Lehner |
2- 3- 11- 83- |
Signs for the Atkin-Lehner involutions |
Class |
32868h |
Isogeny class |
Conductor |
32868 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
30720 |
Modular degree for the optimal curve |
Δ |
-768565722672 = -1 · 24 · 314 · 112 · 83 |
Discriminant |
Eigenvalues |
2- 3- 2 0 11- 4 2 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-2424,-62363] |
[a1,a2,a3,a4,a6] |
Generators |
[3016943:3418416:50653] |
Generators of the group modulo torsion |
j |
-135043612672/65892123 |
j-invariant |
L |
7.0645455535317 |
L(r)(E,1)/r! |
Ω |
0.33247370705775 |
Real period |
R |
10.624216898308 |
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 |
10956c1 |
Quadratic twists by: -3 |