Atkin-Lehner |
2- 3+ 7+ 89- |
Signs for the Atkin-Lehner involutions |
Class |
89712i |
Isogeny class |
Conductor |
89712 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
51840 |
Modular degree for the optimal curve |
Δ |
17461812816 = 24 · 39 · 7 · 892 |
Discriminant |
Eigenvalues |
2- 3+ 2 7+ 0 4 -2 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-864,-7425] |
[a1,a2,a3,a4,a6] |
Generators |
[-857850:2609415:54872] |
Generators of the group modulo torsion |
j |
226492416/55447 |
j-invariant |
L |
7.9580656638566 |
L(r)(E,1)/r! |
Ω |
0.89631659725641 |
Real period |
R |
8.878632496358 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999955151 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
22428b1 89712g1 |
Quadratic twists by: -4 -3 |