Atkin-Lehner |
2- 19+ |
Signs for the Atkin-Lehner involutions |
Class |
1216j |
Isogeny class |
Conductor |
1216 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
384 |
Modular degree for the optimal curve |
Δ |
-159383552 = -1 · 223 · 19 |
Discriminant |
Eigenvalues |
2- -1 4 -3 2 1 3 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-1,-607] |
[a1,a2,a3,a4,a6] |
j |
-1/608 |
j-invariant |
L |
1.6659170043768 |
L(r)(E,1)/r! |
Ω |
0.83295850218839 |
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 |
1216f1 304a1 10944ce1 30400bf1 |
Quadratic twists by: -4 8 -3 5 |