Atkin-Lehner |
3- 7+ 19+ 31+ |
Signs for the Atkin-Lehner involutions |
Class |
12369d |
Isogeny class |
Conductor |
12369 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
1042944 |
Modular degree for the optimal curve |
Δ |
3.2131921748628E+20 |
Discriminant |
Eigenvalues |
-1 3- -4 7+ -2 4 0 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,0,-10144645,12405864776] |
[a1,a2,a3,a4,a6] |
j |
115460724105328254787849681/321319217486278221777 |
j-invariant |
L |
0.51668112701236 |
L(r)(E,1)/r! |
Ω |
0.17222704233745 |
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 |
37107c1 86583p1 |
Quadratic twists by: -3 -7 |