Atkin-Lehner |
2+ 3- 17+ 89+ |
Signs for the Atkin-Lehner involutions |
Class |
36312b |
Isogeny class |
Conductor |
36312 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
18432 |
Modular degree for the optimal curve |
Δ |
31373568 = 28 · 34 · 17 · 89 |
Discriminant |
Eigenvalues |
2+ 3- 2 -4 2 6 17+ 6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-492,4032] |
[a1,a2,a3,a4,a6] |
j |
51553893328/122553 |
j-invariant |
L |
4.1777618159033 |
L(r)(E,1)/r! |
Ω |
2.0888809079567 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
72624a1 108936p1 |
Quadratic twists by: -4 -3 |