Atkin-Lehner |
2- 3- 13+ |
Signs for the Atkin-Lehner involutions |
Class |
12168p |
Isogeny class |
Conductor |
12168 |
Conductor |
∏ cp |
24 |
Product of Tamagawa factors cp |
deg |
49920 |
Modular degree for the optimal curve |
Δ |
-456704790227712 = -1 · 28 · 37 · 138 |
Discriminant |
Eigenvalues |
2- 3- 2 1 6 13+ -8 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-26364,1942148] |
[a1,a2,a3,a4,a6] |
Generators |
[169:1521:1] |
Generators of the group modulo torsion |
j |
-13312/3 |
j-invariant |
L |
5.761913313662 |
L(r)(E,1)/r! |
Ω |
0.50353411965025 |
Real period |
R |
0.47678938136176 |
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 |
24336h1 97344ca1 4056b1 12168e1 |
Quadratic twists by: -4 8 -3 13 |