Atkin-Lehner |
2+ 3+ 67+ |
Signs for the Atkin-Lehner involutions |
Class |
12864a |
Isogeny class |
Conductor |
12864 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
6144 |
Modular degree for the optimal curve |
Δ |
-474218496 = -1 · 218 · 33 · 67 |
Discriminant |
Eigenvalues |
2+ 3+ 1 -5 4 4 6 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-65,1089] |
[a1,a2,a3,a4,a6] |
Generators |
[1:32:1] |
Generators of the group modulo torsion |
j |
-117649/1809 |
j-invariant |
L |
3.9148038239747 |
L(r)(E,1)/r! |
Ω |
1.4046957249238 |
Real period |
R |
0.6967351993947 |
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 |
12864bl1 201b1 38592m1 |
Quadratic twists by: -4 8 -3 |