Atkin-Lehner |
3+ 5+ 11- 71- |
Signs for the Atkin-Lehner involutions |
Class |
128865d |
Isogeny class |
Conductor |
128865 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
502656 |
Modular degree for the optimal curve |
Δ |
-2026093348351875 = -1 · 3 · 54 · 118 · 712 |
Discriminant |
Eigenvalues |
0 3+ 5+ -1 11- -2 0 1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,1,-46141,4402122] |
[a1,a2,a3,a4,a6] |
Generators |
[-64:2662:1] |
Generators of the group modulo torsion |
j |
-50681872384/9451875 |
j-invariant |
L |
3.3468909657176 |
L(r)(E,1)/r! |
Ω |
0.44713180209433 |
Real period |
R |
1.8713111232575 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000318004 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
128865c1 |
Quadratic twists by: -11 |