Atkin-Lehner |
2- 3- 13+ |
Signs for the Atkin-Lehner involutions |
Class |
12168r |
Isogeny class |
Conductor |
12168 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
79872 |
Modular degree for the optimal curve |
Δ |
-49324117344592896 = -1 · 210 · 310 · 138 |
Discriminant |
Eigenvalues |
2- 3- -3 0 0 13+ 1 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,72501,-7597226] |
[a1,a2,a3,a4,a6] |
Generators |
[755:21852:1] |
Generators of the group modulo torsion |
j |
69212/81 |
j-invariant |
L |
3.5881582140727 |
L(r)(E,1)/r! |
Ω |
0.19187026241232 |
Real period |
R |
4.675240145294 |
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 |
24336o1 97344ck1 4056g1 12168g1 |
Quadratic twists by: -4 8 -3 13 |