Atkin-Lehner |
2- 3- 83- |
Signs for the Atkin-Lehner involutions |
Class |
82668c |
Isogeny class |
Conductor |
82668 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
991872 |
Modular degree for the optimal curve |
Δ |
-187564384440301824 = -1 · 28 · 33 · 837 |
Discriminant |
Eigenvalues |
2- 3- 3 2 -3 4 0 7 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-84964,-22942156] |
[a1,a2,a3,a4,a6] |
j |
-810448/2241 |
j-invariant |
L |
6.2251858712716 |
L(r)(E,1)/r! |
Ω |
0.12969137171864 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
4 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
996c1 |
Quadratic twists by: -83 |