Atkin-Lehner |
2- 3- 13+ 17- |
Signs for the Atkin-Lehner involutions |
Class |
68952bb |
Isogeny class |
Conductor |
68952 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
deg |
387072 |
Modular degree for the optimal curve |
Δ |
3971851613160912 = 24 · 34 · 139 · 172 |
Discriminant |
Eigenvalues |
2- 3- 0 -2 2 13+ 17- 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-132383,-18333990] |
[a1,a2,a3,a4,a6] |
j |
3322336000000/51429573 |
j-invariant |
L |
2.0041886536221 |
L(r)(E,1)/r! |
Ω |
0.25052358029686 |
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 |
5304e1 |
Quadratic twists by: 13 |