Atkin-Lehner |
2+ 3+ 67- |
Signs for the Atkin-Lehner involutions |
Class |
12864f |
Isogeny class |
Conductor |
12864 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
4096 |
Modular degree for the optimal curve |
Δ |
13172736 = 216 · 3 · 67 |
Discriminant |
Eigenvalues |
2+ 3+ 2 -2 4 -4 6 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-257,1665] |
[a1,a2,a3,a4,a6] |
j |
28756228/201 |
j-invariant |
L |
2.2520445479133 |
L(r)(E,1)/r! |
Ω |
2.2520445479133 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
12864bi1 1608b1 38592bf1 |
Quadratic twists by: -4 8 -3 |