Atkin-Lehner |
2+ 3+ 7+ 23- |
Signs for the Atkin-Lehner involutions |
Class |
7728b |
Isogeny class |
Conductor |
7728 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
4096 |
Modular degree for the optimal curve |
Δ |
-1892927232 = -1 · 28 · 38 · 72 · 23 |
Discriminant |
Eigenvalues |
2+ 3+ 2 7+ 0 6 -6 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,268,1152] |
[a1,a2,a3,a4,a6] |
j |
8284506032/7394247 |
j-invariant |
L |
1.930551181033 |
L(r)(E,1)/r! |
Ω |
0.96527559051648 |
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 |
3864e1 30912cb1 23184e1 54096u1 |
Quadratic twists by: -4 8 -3 -7 |