Atkin-Lehner |
2+ 3- 89+ |
Signs for the Atkin-Lehner involutions |
Class |
51264l |
Isogeny class |
Conductor |
51264 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
30720 |
Modular degree for the optimal curve |
Δ |
17008164864 = 218 · 36 · 89 |
Discriminant |
Eigenvalues |
2+ 3- -2 2 -4 -2 -6 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-876,-7760] |
[a1,a2,a3,a4,a6] |
Generators |
[-19:45:1] [-12:32:1] |
Generators of the group modulo torsion |
j |
389017/89 |
j-invariant |
L |
8.910292302634 |
L(r)(E,1)/r! |
Ω |
0.89197921412164 |
Real period |
R |
4.994674854283 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000001 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
51264bb1 801b1 5696g1 |
Quadratic twists by: -4 8 -3 |