Atkin-Lehner |
2- 3+ 11+ 13- |
Signs for the Atkin-Lehner involutions |
Class |
82368ct |
Isogeny class |
Conductor |
82368 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
135168 |
Modular degree for the optimal curve |
Δ |
3116941933248 = 26 · 39 · 114 · 132 |
Discriminant |
Eigenvalues |
2- 3+ 0 4 11+ 13- 4 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-4995,106056] |
[a1,a2,a3,a4,a6] |
Generators |
[-10668:164970:343] |
Generators of the group modulo torsion |
j |
10941048000/2474329 |
j-invariant |
L |
8.2567373381711 |
L(r)(E,1)/r! |
Ω |
0.75266802474365 |
Real period |
R |
5.4849794779478 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999991744 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
82368de1 41184u2 82368dd1 |
Quadratic twists by: -4 8 -3 |