Atkin-Lehner |
2- 3- 11+ 13+ |
Signs for the Atkin-Lehner involutions |
Class |
82368dq |
Isogeny class |
Conductor |
82368 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
196608 |
Modular degree for the optimal curve |
Δ |
10568143872 = 210 · 38 · 112 · 13 |
Discriminant |
Eigenvalues |
2- 3- -2 0 11+ 13+ -2 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-169896,26953976] |
[a1,a2,a3,a4,a6] |
Generators |
[241:81:1] |
Generators of the group modulo torsion |
j |
726516846671872/14157 |
j-invariant |
L |
5.0319021758714 |
L(r)(E,1)/r! |
Ω |
0.92297552928755 |
Real period |
R |
1.3629565510519 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999989253 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
82368bu1 20592n1 27456br1 |
Quadratic twists by: -4 8 -3 |