Atkin-Lehner |
2+ 3- 13+ |
Signs for the Atkin-Lehner involutions |
Class |
8112k |
Isogeny class |
Conductor |
8112 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
2304 |
Modular degree for the optimal curve |
Δ |
-231686832 = -1 · 24 · 3 · 136 |
Discriminant |
Eigenvalues |
2+ 3- 2 0 4 13+ 2 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,113,-532] |
[a1,a2,a3,a4,a6] |
j |
2048/3 |
j-invariant |
L |
3.7403442104052 |
L(r)(E,1)/r! |
Ω |
0.9350860526013 |
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 |
4056a1 32448ci1 24336i1 48a4 |
Quadratic twists by: -4 8 -3 13 |