Atkin-Lehner |
2- 3+ 13+ 31+ |
Signs for the Atkin-Lehner involutions |
Class |
9672g |
Isogeny class |
Conductor |
9672 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
58752 |
Modular degree for the optimal curve |
Δ |
24626401488 = 24 · 36 · 133 · 312 |
Discriminant |
Eigenvalues |
2- 3+ 0 -4 -2 13+ -2 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-703763,-227007132] |
[a1,a2,a3,a4,a6] |
j |
2409259817702320384000/1539150093 |
j-invariant |
L |
0.32966503804269 |
L(r)(E,1)/r! |
Ω |
0.16483251902134 |
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 |
19344f1 77376u1 29016c1 125736e1 |
Quadratic twists by: -4 8 -3 13 |