Atkin-Lehner |
19- |
Signs for the Atkin-Lehner involutions |
Class |
19a |
Isogeny class |
Conductor |
19 |
Conductor |
∏ cp |
3 |
Product of Tamagawa factors cp |
deg |
1 |
Modular degree for the optimal curve |
Δ |
-6859 = -1 · 193 |
Discriminant |
Eigenvalues |
0 -2 3 -1 3 -4 -3 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,1,-9,-15] |
[a1,a2,a3,a4,a6] |
j |
-89915392/6859 |
j-invariant |
L |
0.4532532444961 |
L(r)(E,1)/r! |
Ω |
1.3597597334883 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
3 |
Number of elements in the torsion subgroup |
Twists |
304e2 1216d2 171b2 475a2 |
Quadratic twists by: -4 8 -3 5 |