Atkin-Lehner |
2+ 7- 29- |
Signs for the Atkin-Lehner involutions |
Class |
12992u |
Isogeny class |
Conductor |
12992 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
6144 |
Modular degree for the optimal curve |
Δ |
-1543241728 = -1 · 218 · 7 · 292 |
Discriminant |
Eigenvalues |
2+ -2 -2 7- 4 2 4 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-609,5887] |
[a1,a2,a3,a4,a6] |
Generators |
[3:64:1] |
Generators of the group modulo torsion |
j |
-95443993/5887 |
j-invariant |
L |
3.0431147915581 |
L(r)(E,1)/r! |
Ω |
1.4839388163276 |
Real period |
R |
1.0253504922423 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
12992be1 203c1 116928cb1 90944ca1 |
Quadratic twists by: -4 8 -3 -7 |