Atkin-Lehner |
19+ 41+ |
Signs for the Atkin-Lehner involutions |
Class |
31939b |
Isogeny class |
Conductor |
31939 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
23040 |
Modular degree for the optimal curve |
Δ |
-90251980579 = -1 · 19 · 416 |
Discriminant |
Eigenvalues |
0 2 3 1 -3 4 3 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,1,1121,-1012] |
[a1,a2,a3,a4,a6] |
Generators |
[480012:4987592:4913] |
Generators of the group modulo torsion |
j |
32768/19 |
j-invariant |
L |
8.5410341075109 |
L(r)(E,1)/r! |
Ω |
0.63707637853055 |
Real period |
R |
6.7033046549388 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
19a3 |
Quadratic twists by: 41 |