Atkin-Lehner |
2- 11- 67- |
Signs for the Atkin-Lehner involutions |
Class |
129712x |
Isogeny class |
Conductor |
129712 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
691200 |
Modular degree for the optimal curve |
Δ |
342265811959808 = 218 · 117 · 67 |
Discriminant |
Eigenvalues |
2- 0 4 4 11- 2 2 8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-24563,-1184590] |
[a1,a2,a3,a4,a6] |
j |
225866529/47168 |
j-invariant |
L |
6.1915444545637 |
L(r)(E,1)/r! |
Ω |
0.38697146217771 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
4 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
16214c1 11792c1 |
Quadratic twists by: -4 -11 |