Atkin-Lehner |
2- 3+ 11- 23- |
Signs for the Atkin-Lehner involutions |
Class |
69828s |
Isogeny class |
Conductor |
69828 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
126720 |
Modular degree for the optimal curve |
Δ |
-1797747836016 = -1 · 24 · 3 · 11 · 237 |
Discriminant |
Eigenvalues |
2- 3+ -3 -3 11- -2 0 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,2998,12069] |
[a1,a2,a3,a4,a6] |
j |
1257728/759 |
j-invariant |
L |
1.0263135872817 |
L(r)(E,1)/r! |
Ω |
0.51315679492694 |
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 |
3036c1 |
Quadratic twists by: -23 |