Atkin-Lehner |
2+ 3- 13+ 23+ |
Signs for the Atkin-Lehner involutions |
Class |
69966f |
Isogeny class |
Conductor |
69966 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
deg |
516096 |
Modular degree for the optimal curve |
Δ |
-9245893331328732 = -1 · 22 · 36 · 1310 · 23 |
Discriminant |
Eigenvalues |
2+ 3- 0 0 -2 13+ 2 6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-170637,-27479503] |
[a1,a2,a3,a4,a6] |
j |
-156155441625/2627612 |
j-invariant |
L |
0.93865772151478 |
L(r)(E,1)/r! |
Ω |
0.11733221384376 |
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 |
7774c1 5382i1 |
Quadratic twists by: -3 13 |