Atkin-Lehner |
2+ 3+ 13- 37+ |
Signs for the Atkin-Lehner involutions |
Class |
69264d |
Isogeny class |
Conductor |
69264 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
29184 |
Modular degree for the optimal curve |
Δ |
-2423685888 = -1 · 28 · 39 · 13 · 37 |
Discriminant |
Eigenvalues |
2+ 3+ -2 0 3 13- -7 1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,324,-756] |
[a1,a2,a3,a4,a6] |
j |
746496/481 |
j-invariant |
L |
1.6602950619366 |
L(r)(E,1)/r! |
Ω |
0.83014753841353 |
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 |
34632b1 69264c1 |
Quadratic twists by: -4 -3 |