Atkin-Lehner |
2- 31- 67+ |
Signs for the Atkin-Lehner involutions |
Class |
8308b |
Isogeny class |
Conductor |
8308 |
Conductor |
∏ cp |
30 |
Product of Tamagawa factors cp |
deg |
9600 |
Modular degree for the optimal curve |
Δ |
-2056260141424 = -1 · 24 · 315 · 672 |
Discriminant |
Eigenvalues |
2- 0 -1 1 0 6 4 -5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-8393,303889] |
[a1,a2,a3,a4,a6] |
Generators |
[117:961:1] |
Generators of the group modulo torsion |
j |
-4086536655446784/128516258839 |
j-invariant |
L |
4.0868138108657 |
L(r)(E,1)/r! |
Ω |
0.82329655707663 |
Real period |
R |
0.16546543995347 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
33232g1 74772d1 |
Quadratic twists by: -4 -3 |