Atkin-Lehner |
2+ 3- 61+ |
Signs for the Atkin-Lehner involutions |
Class |
11712m |
Isogeny class |
Conductor |
11712 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
15360 |
Modular degree for the optimal curve |
Δ |
-147371065344 = -1 · 228 · 32 · 61 |
Discriminant |
Eigenvalues |
2+ 3- 3 -3 1 5 2 8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-2049,39519] |
[a1,a2,a3,a4,a6] |
j |
-3630961153/562176 |
j-invariant |
L |
3.9767241195864 |
L(r)(E,1)/r! |
Ω |
0.99418102989659 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
11712x1 366g1 35136t1 |
Quadratic twists by: -4 8 -3 |