Atkin-Lehner |
2- 3- 11- 13+ |
Signs for the Atkin-Lehner involutions |
Class |
82368es |
Isogeny class |
Conductor |
82368 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
4055040 |
Modular degree for the optimal curve |
Δ |
-1.1652909606745E+21 |
Discriminant |
Eigenvalues |
2- 3- -3 -1 11- 13+ 8 -6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-329484,1643998736] |
[a1,a2,a3,a4,a6] |
j |
-20699471212993/6097712265216 |
j-invariant |
L |
0.50173313987676 |
L(r)(E,1)/r! |
Ω |
0.12543327878391 |
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 |
82368y1 20592bh1 27456bk1 |
Quadratic twists by: -4 8 -3 |