Atkin-Lehner |
2+ 3- 13- |
Signs for the Atkin-Lehner involutions |
Class |
12168k |
Isogeny class |
Conductor |
12168 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
239616 |
Modular degree for the optimal curve |
Δ |
811535868185254992 = 24 · 314 · 139 |
Discriminant |
Eigenvalues |
2+ 3- -4 2 2 13- -6 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-540462,-146660735] |
[a1,a2,a3,a4,a6] |
Generators |
[6920:572265:1] |
Generators of the group modulo torsion |
j |
141150208/6561 |
j-invariant |
L |
3.714574565672 |
L(r)(E,1)/r! |
Ω |
0.1765862113438 |
Real period |
R |
5.2588683700226 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
24336x1 97344do1 4056s1 12168x1 |
Quadratic twists by: -4 8 -3 13 |