Atkin-Lehner |
2+ 19- 59+ |
Signs for the Atkin-Lehner involutions |
Class |
8968a |
Isogeny class |
Conductor |
8968 |
Conductor |
∏ cp |
24 |
Product of Tamagawa factors cp |
deg |
3744 |
Modular degree for the optimal curve |
Δ |
-6112301824 = -1 · 28 · 193 · 592 |
Discriminant |
Eigenvalues |
2+ 0 -1 -3 -1 -6 -3 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-668,7636] |
[a1,a2,a3,a4,a6] |
Generators |
[246:3838:1] [-12:118:1] |
Generators of the group modulo torsion |
j |
-128769537024/23876179 |
j-invariant |
L |
5.10244904031 |
L(r)(E,1)/r! |
Ω |
1.2898607124278 |
Real period |
R |
0.16482558255927 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000001 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
17936a1 71744a1 80712m1 |
Quadratic twists by: -4 8 -3 |