Atkin-Lehner |
2+ 3- 11- 13- |
Signs for the Atkin-Lehner involutions |
Class |
82368cj |
Isogeny class |
Conductor |
82368 |
Conductor |
∏ cp |
96 |
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 |
5.4205489051901 |
L(r)(E,1)/r! |
Ω |
0.22585620345833 |
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 |
82368eh1 2574f1 27456k1 |
Quadratic twists by: -4 8 -3 |