Atkin-Lehner |
2- 3+ 7- 19+ |
Signs for the Atkin-Lehner involutions |
Class |
12768n |
Isogeny class |
Conductor |
12768 |
Conductor |
∏ cp |
48 |
Product of Tamagawa factors cp |
deg |
24576 |
Modular degree for the optimal curve |
Δ |
220171162176 = 26 · 34 · 76 · 192 |
Discriminant |
Eigenvalues |
2- 3+ 2 7- 0 -2 -6 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-39102,2989080] |
[a1,a2,a3,a4,a6] |
Generators |
[122:140:1] |
Generators of the group modulo torsion |
j |
103312235477340352/3440174409 |
j-invariant |
L |
4.5437988246743 |
L(r)(E,1)/r! |
Ω |
0.93034817941621 |
Real period |
R |
1.6279922310109 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
4 |
Number of elements in the torsion subgroup |
Twists |
12768z1 25536do2 38304r1 89376cx1 |
Quadratic twists by: -4 8 -3 -7 |