Atkin-Lehner |
2- 3+ 11+ 61+ |
Signs for the Atkin-Lehner involutions |
Class |
12078o |
Isogeny class |
Conductor |
12078 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
deg |
115200 |
Modular degree for the optimal curve |
Δ |
34232723712 = 28 · 33 · 113 · 612 |
Discriminant |
Eigenvalues |
2- 3+ -4 -2 11+ 6 -6 6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-309557,-66214195] |
[a1,a2,a3,a4,a6] |
j |
121501186819203686643/1267878656 |
j-invariant |
L |
1.619214910105 |
L(r)(E,1)/r! |
Ω |
0.20240186376313 |
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 |
96624bb1 12078d1 |
Quadratic twists by: -4 -3 |