Atkin-Lehner |
2- 7- 13- |
Signs for the Atkin-Lehner involutions |
Class |
40768dn |
Isogeny class |
Conductor |
40768 |
Conductor |
∏ cp |
48 |
Product of Tamagawa factors cp |
deg |
276480 |
Modular degree for the optimal curve |
Δ |
-142350314844028928 = -1 · 215 · 711 · 133 |
Discriminant |
Eigenvalues |
2- -1 0 7- -1 13- -4 -6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,123807,-6996191] |
[a1,a2,a3,a4,a6] |
Generators |
[96:2401:1] [201:-5096:1] |
Generators of the group modulo torsion |
j |
54439939000/36924979 |
j-invariant |
L |
7.5375570354401 |
L(r)(E,1)/r! |
Ω |
0.18529402582606 |
Real period |
R |
0.84747707077043 |
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 |
40768di1 20384d1 5824z1 |
Quadratic twists by: -4 8 -7 |