Atkin-Lehner |
2+ 7+ 29- |
Signs for the Atkin-Lehner involutions |
Class |
12992i |
Isogeny class |
Conductor |
12992 |
Conductor |
∏ cp |
1 |
Product of Tamagawa factors cp |
deg |
4608 |
Modular degree for the optimal curve |
Δ |
-162971648 = -1 · 214 · 73 · 29 |
Discriminant |
Eigenvalues |
2+ -3 0 7+ -2 0 2 -1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-160,-992] |
[a1,a2,a3,a4,a6] |
j |
-27648000/9947 |
j-invariant |
L |
0.65928825431809 |
L(r)(E,1)/r! |
Ω |
0.65928825431809 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
12992bm1 812a1 116928u1 90944ck1 |
Quadratic twists by: -4 8 -3 -7 |