Atkin-Lehner |
2+ 3- 11- 13+ |
Signs for the Atkin-Lehner involutions |
Class |
82368bt |
Isogeny class |
Conductor |
82368 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
45056 |
Modular degree for the optimal curve |
Δ |
-14090858496 = -1 · 212 · 37 · 112 · 13 |
Discriminant |
Eigenvalues |
2+ 3- -2 0 11- 13+ 0 -6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,204,-5600] |
[a1,a2,a3,a4,a6] |
Generators |
[36:220:1] |
Generators of the group modulo torsion |
j |
314432/4719 |
j-invariant |
L |
4.8736688332244 |
L(r)(E,1)/r! |
Ω |
0.61245963956389 |
Real period |
R |
1.989383675747 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.9999999994286 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
82368v1 41184ba1 27456w1 |
Quadratic twists by: -4 8 -3 |