Atkin-Lehner |
2- 3+ 43- |
Signs for the Atkin-Lehner involutions |
Class |
12384k |
Isogeny class |
Conductor |
12384 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
2048 |
Modular degree for the optimal curve |
Δ |
-4755456 = -1 · 212 · 33 · 43 |
Discriminant |
Eigenvalues |
2- 3+ -3 3 1 -5 2 -1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,36,64] |
[a1,a2,a3,a4,a6] |
Generators |
[2:12:1] |
Generators of the group modulo torsion |
j |
46656/43 |
j-invariant |
L |
4.0466897773077 |
L(r)(E,1)/r! |
Ω |
1.5947141758686 |
Real period |
R |
0.31719553874783 |
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 |
12384j1 24768bp1 12384b1 |
Quadratic twists by: -4 8 -3 |