Atkin-Lehner |
2- 3+ 13- 29- |
Signs for the Atkin-Lehner involutions |
Class |
72384cr |
Isogeny class |
Conductor |
72384 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
208896 |
Modular degree for the optimal curve |
Δ |
-986701627392 = -1 · 226 · 3 · 132 · 29 |
Discriminant |
Eigenvalues |
2- 3+ 4 4 4 13- -2 6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-4321,-117887] |
[a1,a2,a3,a4,a6] |
j |
-34043726521/3763968 |
j-invariant |
L |
5.2667094862713 |
L(r)(E,1)/r! |
Ω |
0.29259497151522 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
9 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
72384bn1 18096bc1 |
Quadratic twists by: -4 8 |