Atkin-Lehner |
3- 19+ 71- |
Signs for the Atkin-Lehner involutions |
Class |
12141f |
Isogeny class |
Conductor |
12141 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
34176 |
Modular degree for the optimal curve |
Δ |
-9929974553559 = -1 · 318 · 192 · 71 |
Discriminant |
Eigenvalues |
1 3- 2 -4 -4 6 -6 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,2619,141912] |
[a1,a2,a3,a4,a6] |
Generators |
[1992:87924:1] |
Generators of the group modulo torsion |
j |
2724641702063/13621364271 |
j-invariant |
L |
5.2608240093415 |
L(r)(E,1)/r! |
Ω |
0.52153823792705 |
Real period |
R |
5.04356500326 |
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 |
4047a1 |
Quadratic twists by: -3 |