Atkin-Lehner |
2+ 5+ 7+ 31+ |
Signs for the Atkin-Lehner involutions |
Class |
8680b |
Isogeny class |
Conductor |
8680 |
Conductor |
∏ cp |
1 |
Product of Tamagawa factors cp |
deg |
14784 |
Modular degree for the optimal curve |
Δ |
21700000000000 = 211 · 511 · 7 · 31 |
Discriminant |
Eigenvalues |
2+ -1 5+ 7+ 3 1 -4 1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-16136,761836] |
[a1,a2,a3,a4,a6] |
Generators |
[33:514:1] |
Generators of the group modulo torsion |
j |
226886329763858/10595703125 |
j-invariant |
L |
3.076014681794 |
L(r)(E,1)/r! |
Ω |
0.67178688931582 |
Real period |
R |
4.5788548879344 |
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 |
17360e1 69440ba1 78120bg1 43400p1 |
Quadratic twists by: -4 8 -3 5 |