Atkin-Lehner |
2- 3- 11- 13- |
Signs for the Atkin-Lehner involutions |
Class |
82368fc |
Isogeny class |
Conductor |
82368 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
deg |
884736 |
Modular degree for the optimal curve |
Δ |
39288961738211328 = 230 · 39 · 11 · 132 |
Discriminant |
Eigenvalues |
2- 3- 2 -4 11- 13- -2 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-614604,185210768] |
[a1,a2,a3,a4,a6] |
Generators |
[469:351:1] |
Generators of the group modulo torsion |
j |
134351465835313/205590528 |
j-invariant |
L |
6.0621989514711 |
L(r)(E,1)/r! |
Ω |
0.36337669475367 |
Real period |
R |
2.0853700289847 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000006111 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
82368bh1 20592bc1 27456bo1 |
Quadratic twists by: -4 8 -3 |