Atkin-Lehner |
2+ 3- 11- |
Signs for the Atkin-Lehner involutions |
Class |
69696cl |
Isogeny class |
Conductor |
69696 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
81920 |
Modular degree for the optimal curve |
Δ |
247961850048 = 26 · 37 · 116 |
Discriminant |
Eigenvalues |
2+ 3- 2 4 11- -2 -6 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-4719,-122452] |
[a1,a2,a3,a4,a6] |
Generators |
[-12292:8660:343] |
Generators of the group modulo torsion |
j |
140608/3 |
j-invariant |
L |
8.4831078867942 |
L(r)(E,1)/r! |
Ω |
0.57676737888305 |
Real period |
R |
7.3540115105483 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.000000000043 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
69696co1 34848ba3 23232u1 576c1 |
Quadratic twists by: -4 8 -3 -11 |