Atkin-Lehner |
2- 3- 11+ 13+ |
Signs for the Atkin-Lehner involutions |
Class |
82368dm |
Isogeny class |
Conductor |
82368 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
261120 |
Modular degree for the optimal curve |
Δ |
-97563396243456 = -1 · 215 · 36 · 11 · 135 |
Discriminant |
Eigenvalues |
2- 3- 1 -5 11+ 13+ -6 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,11508,7472] |
[a1,a2,a3,a4,a6] |
Generators |
[52:864:1] |
Generators of the group modulo torsion |
j |
7055792632/4084223 |
j-invariant |
L |
4.496545168001 |
L(r)(E,1)/r! |
Ω |
0.35875638741417 |
Real period |
R |
3.1334251624465 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000004344 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
82368eo1 41184o1 9152bc1 |
Quadratic twists by: -4 8 -3 |