Atkin-Lehner |
2- 3- 11+ 13- |
Signs for the Atkin-Lehner involutions |
Class |
82368ek |
Isogeny class |
Conductor |
82368 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
245760 |
Modular degree for the optimal curve |
Δ |
-3935192481792 = -1 · 222 · 38 · 11 · 13 |
Discriminant |
Eigenvalues |
2- 3- 4 4 11+ 13- -4 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-588,-95600] |
[a1,a2,a3,a4,a6] |
j |
-117649/20592 |
j-invariant |
L |
5.5821362229691 |
L(r)(E,1)/r! |
Ω |
0.34888351935018 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
4 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
82368co1 20592bp1 27456cp1 |
Quadratic twists by: -4 8 -3 |