Atkin-Lehner |
2+ 3- 19- |
Signs for the Atkin-Lehner involutions |
Class |
69312br |
Isogeny class |
Conductor |
69312 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
276480 |
Modular degree for the optimal curve |
Δ |
702969339445248 = 218 · 3 · 197 |
Discriminant |
Eigenvalues |
2+ 3- 2 0 0 6 -6 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-35137,2179103] |
[a1,a2,a3,a4,a6] |
Generators |
[254859:49929472:35937] |
Generators of the group modulo torsion |
j |
389017/57 |
j-invariant |
L |
9.8985625448167 |
L(r)(E,1)/r! |
Ω |
0.48797694649087 |
Real period |
R |
10.142448957349 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000529 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
69312cp1 1083b1 3648g1 |
Quadratic twists by: -4 8 -19 |