Atkin-Lehner |
2- 3- 11+ 13- |
Signs for the Atkin-Lehner involutions |
Class |
82368eh |
Isogeny class |
Conductor |
82368 |
Conductor |
∏ cp |
48 |
Product of Tamagawa factors cp |
deg |
1548288 |
Modular degree for the optimal curve |
Δ |
-2497031790472986624 = -1 · 232 · 37 · 112 · 133 |
Discriminant |
Eigenvalues |
2- 3- 2 -4 11+ 13- 8 -6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-191244,-82561520] |
[a1,a2,a3,a4,a6] |
j |
-4047806261953/13066420224 |
j-invariant |
L |
1.2621604097493 |
L(r)(E,1)/r! |
Ω |
0.1051800319112 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
82368cj1 20592bo1 27456co1 |
Quadratic twists by: -4 8 -3 |