Atkin-Lehner |
2+ 3- 89+ |
Signs for the Atkin-Lehner involutions |
Class |
51264k |
Isogeny class |
Conductor |
51264 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
30720 |
Modular degree for the optimal curve |
Δ |
4252041216 = 216 · 36 · 89 |
Discriminant |
Eigenvalues |
2+ 3- 2 -4 0 -4 -2 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-1164,14960] |
[a1,a2,a3,a4,a6] |
Generators |
[-28:160:1] [-10:160:1] |
Generators of the group modulo torsion |
j |
3650692/89 |
j-invariant |
L |
9.782410973836 |
L(r)(E,1)/r! |
Ω |
1.381403137754 |
Real period |
R |
3.5407516844584 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999985 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
51264z1 6408c1 5696f1 |
Quadratic twists by: -4 8 -3 |