Atkin-Lehner |
2- 31+ 43+ |
Signs for the Atkin-Lehner involutions |
Class |
85312l |
Isogeny class |
Conductor |
85312 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
82944 |
Modular degree for the optimal curve |
Δ |
178912231424 = 227 · 31 · 43 |
Discriminant |
Eigenvalues |
2- 0 1 2 5 1 2 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-13292,-589488] |
[a1,a2,a3,a4,a6] |
j |
990728800209/682496 |
j-invariant |
L |
3.5572132677384 |
L(r)(E,1)/r! |
Ω |
0.44465167233711 |
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 |
85312j1 21328h1 |
Quadratic twists by: -4 8 |