Atkin-Lehner |
2+ 11+ 89+ |
Signs for the Atkin-Lehner involutions |
Class |
31328a |
Isogeny class |
Conductor |
31328 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
9600 |
Modular degree for the optimal curve |
Δ |
-485208064 = -1 · 212 · 113 · 89 |
Discriminant |
Eigenvalues |
2+ 0 3 -4 11+ 1 2 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-56,1072] |
[a1,a2,a3,a4,a6] |
Generators |
[-12:4:1] |
Generators of the group modulo torsion |
j |
-4741632/118459 |
j-invariant |
L |
5.3596143682115 |
L(r)(E,1)/r! |
Ω |
1.3896305616496 |
Real period |
R |
1.9284313817367 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000001 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
31328d1 62656r1 |
Quadratic twists by: -4 8 |