Atkin-Lehner |
2- 3- 11- |
Signs for the Atkin-Lehner involutions |
Class |
69696gj |
Isogeny class |
Conductor |
69696 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
deg |
184320 |
Modular degree for the optimal curve |
Δ |
-130923856825344 = -1 · 210 · 38 · 117 |
Discriminant |
Eigenvalues |
2- 3- 2 -2 11- -2 4 6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,11616,266200] |
[a1,a2,a3,a4,a6] |
j |
131072/99 |
j-invariant |
L |
2.9938210366762 |
L(r)(E,1)/r! |
Ω |
0.37422762835289 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
69696ci1 17424by1 23232dr1 6336ca1 |
Quadratic twists by: -4 8 -3 -11 |