Atkin-Lehner |
2+ 3+ 7+ 19- |
Signs for the Atkin-Lehner involutions |
Class |
3192c |
Isogeny class |
Conductor |
3192 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
6144 |
Modular degree for the optimal curve |
Δ |
4488567692112 = 24 · 316 · 73 · 19 |
Discriminant |
Eigenvalues |
2+ 3+ -2 7+ -4 2 -6 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-4359,-41940] |
[a1,a2,a3,a4,a6] |
j |
572616640141312/280535480757 |
j-invariant |
L |
0.61750109449595 |
L(r)(E,1)/r! |
Ω |
0.61750109449595 |
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 |
6384n1 25536bb1 9576v1 79800bu1 |
Quadratic twists by: -4 8 -3 5 |