Atkin-Lehner |
3+ 7+ 19+ 31- |
Signs for the Atkin-Lehner involutions |
Class |
12369b |
Isogeny class |
Conductor |
12369 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
8192 |
Modular degree for the optimal curve |
Δ |
2684073 = 3 · 72 · 19 · 312 |
Discriminant |
Eigenvalues |
1 3+ 4 7+ 6 4 -4 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,0,-1143,-15360] |
[a1,a2,a3,a4,a6] |
j |
165369706597369/2684073 |
j-invariant |
L |
3.2839682424703 |
L(r)(E,1)/r! |
Ω |
0.82099206061757 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
4 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
37107f1 86583x1 |
Quadratic twists by: -3 -7 |