Atkin-Lehner |
2+ 3- 11- 13+ |
Signs for the Atkin-Lehner involutions |
Class |
82368bz |
Isogeny class |
Conductor |
82368 |
Conductor |
∏ cp |
6 |
Product of Tamagawa factors cp |
deg |
115200 |
Modular degree for the optimal curve |
Δ |
-2686657019904 = -1 · 214 · 36 · 113 · 132 |
Discriminant |
Eigenvalues |
2+ 3- 3 2 11- 13+ 0 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,3264,32672] |
[a1,a2,a3,a4,a6] |
Generators |
[353:6721:1] |
Generators of the group modulo torsion |
j |
321978368/224939 |
j-invariant |
L |
9.4196426956481 |
L(r)(E,1)/r! |
Ω |
0.51171020572686 |
Real period |
R |
3.0680264559339 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000002123 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
82368dv1 5148d1 9152c1 |
Quadratic twists by: -4 8 -3 |