Atkin-Lehner |
2+ 3- 11- |
Signs for the Atkin-Lehner involutions |
Class |
8712n |
Isogeny class |
Conductor |
8712 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
322560 |
Modular degree for the optimal curve |
Δ |
31814497208558592 = 210 · 313 · 117 |
Discriminant |
Eigenvalues |
2+ 3- -4 2 11- 0 -6 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-8729787,-9927809210] |
[a1,a2,a3,a4,a6] |
Generators |
[-1416601714:-47285469:830584] |
Generators of the group modulo torsion |
j |
55635379958596/24057 |
j-invariant |
L |
3.3470315298314 |
L(r)(E,1)/r! |
Ω |
0.087831167182078 |
Real period |
R |
9.52689016102 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
17424z1 69696do1 2904o1 792g1 |
Quadratic twists by: -4 8 -3 -11 |