Atkin-Lehner |
2- 3+ 7- 11+ 29- |
Signs for the Atkin-Lehner involutions |
Class |
13398bb |
Isogeny class |
Conductor |
13398 |
Conductor |
∏ cp |
192 |
Product of Tamagawa factors cp |
deg |
122880 |
Modular degree for the optimal curve |
Δ |
-34348019264520192 = -1 · 224 · 35 · 74 · 112 · 29 |
Discriminant |
Eigenvalues |
2- 3+ 2 7- 11+ -2 2 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,1,-49137,9832719] |
[a1,a2,a3,a4,a6] |
j |
-13120493711215846033/34348019264520192 |
j-invariant |
L |
3.8976728608509 |
L(r)(E,1)/r! |
Ω |
0.32480607173757 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
4 |
Number of elements in the torsion subgroup |
Twists |
107184ck1 40194u1 93786cy1 |
Quadratic twists by: -4 -3 -7 |