Atkin-Lehner |
2+ 7+ 89- |
Signs for the Atkin-Lehner involutions |
Class |
8722b |
Isogeny class |
Conductor |
8722 |
Conductor |
∏ cp |
9 |
Product of Tamagawa factors cp |
deg |
21504 |
Modular degree for the optimal curve |
Δ |
-8128011992338 = -1 · 2 · 78 · 893 |
Discriminant |
Eigenvalues |
2+ -2 0 7+ -3 2 -3 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,1,-13256,-604320] |
[a1,a2,a3,a4,a6] |
j |
-44681709625/1409938 |
j-invariant |
L |
0.22205678824207 |
L(r)(E,1)/r! |
Ω |
0.22205678824207 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
3 |
Number of elements in the torsion subgroup |
Twists |
69776f1 78498bk1 8722f1 |
Quadratic twists by: -4 -3 -7 |