Atkin-Lehner |
2- 19+ |
Signs for the Atkin-Lehner involutions |
Class |
1216k |
Isogeny class |
Conductor |
1216 |
Conductor |
∏ cp |
1 |
Product of Tamagawa factors cp |
deg |
192 |
Modular degree for the optimal curve |
Δ |
-311296 = -1 · 214 · 19 |
Discriminant |
Eigenvalues |
2- 2 1 3 5 4 -3 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-85,333] |
[a1,a2,a3,a4,a6] |
j |
-4194304/19 |
j-invariant |
L |
3.0762060701908 |
L(r)(E,1)/r! |
Ω |
3.0762060701908 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
1216h1 304f1 10944bw1 30400bj1 |
Quadratic twists by: -4 8 -3 5 |