Atkin-Lehner |
2- 3- 11+ |
Signs for the Atkin-Lehner involutions |
Class |
69696ff |
Isogeny class |
Conductor |
69696 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
73728 |
Modular degree for the optimal curve |
Δ |
429229228032 = 214 · 39 · 113 |
Discriminant |
Eigenvalues |
2- 3- -2 2 11+ -4 2 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-3036,-56144] |
[a1,a2,a3,a4,a6] |
Generators |
[-40:36:1] |
Generators of the group modulo torsion |
j |
194672/27 |
j-invariant |
L |
5.1625029058802 |
L(r)(E,1)/r! |
Ω |
0.64909054321644 |
Real period |
R |
1.9883600832727 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999992924 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
69696be1 17424i1 23232dh1 69696fg1 |
Quadratic twists by: -4 8 -3 -11 |