Atkin-Lehner |
3- 7- 13- 61+ |
Signs for the Atkin-Lehner involutions |
Class |
49959h |
Isogeny class |
Conductor |
49959 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
691200 |
Modular degree for the optimal curve |
Δ |
-62931472800304563 = -1 · 314 · 73 · 132 · 613 |
Discriminant |
Eigenvalues |
2 3- -2 7- 2 13- -5 6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,1,-233481,45069727] |
[a1,a2,a3,a4,a6] |
j |
-1930860143445127168/86325751440747 |
j-invariant |
L |
4.1569181158481 |
L(r)(E,1)/r! |
Ω |
0.34640984297256 |
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 |
16653e1 |
Quadratic twists by: -3 |