Atkin-Lehner |
2- 3- 7- 19+ |
Signs for the Atkin-Lehner involutions |
Class |
12768bc |
Isogeny class |
Conductor |
12768 |
Conductor |
∏ cp |
96 |
Product of Tamagawa factors cp |
deg |
67584 |
Modular degree for the optimal curve |
Δ |
217192845151296 = 26 · 312 · 72 · 194 |
Discriminant |
Eigenvalues |
2- 3- 2 7- 0 -6 2 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-175462,28222040] |
[a1,a2,a3,a4,a6] |
j |
9334594126684326592/3393638205489 |
j-invariant |
L |
3.3028558608828 |
L(r)(E,1)/r! |
Ω |
0.55047597681381 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
4 |
Number of elements in the torsion subgroup |
Twists |
12768m1 25536cn2 38304s1 89376by1 |
Quadratic twists by: -4 8 -3 -7 |