Atkin-Lehner |
2- 3- 89+ |
Signs for the Atkin-Lehner involutions |
Class |
12816j |
Isogeny class |
Conductor |
12816 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
137088 |
Modular degree for the optimal curve |
Δ |
-34319330982309888 = -1 · 212 · 323 · 89 |
Discriminant |
Eigenvalues |
2- 3- -4 2 2 6 -4 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-63552,10838320] |
[a1,a2,a3,a4,a6] |
Generators |
[19940:295245:64] |
Generators of the group modulo torsion |
j |
-9506571157504/11493474507 |
j-invariant |
L |
4.0359447785706 |
L(r)(E,1)/r! |
Ω |
0.33283520523709 |
Real period |
R |
3.0314887931519 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
801a1 51264be1 4272e1 |
Quadratic twists by: -4 8 -3 |