Atkin-Lehner |
2+ 11+ 13+ 41+ |
Signs for the Atkin-Lehner involutions |
Class |
128986a |
Isogeny class |
Conductor |
128986 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
1658880 |
Modular degree for the optimal curve |
Δ |
-1707906039594287104 = -1 · 216 · 113 · 132 · 415 |
Discriminant |
Eigenvalues |
2+ 0 -1 -1 11+ 13+ 7 1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,86740,-62124848] |
[a1,a2,a3,a4,a6] |
Generators |
[696:17956:1] |
Generators of the group modulo torsion |
j |
54225191412885501/1283175086096384 |
j-invariant |
L |
2.9989746688414 |
L(r)(E,1)/r! |
Ω |
0.12869300670905 |
Real period |
R |
2.9129152283003 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.000000038911 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
128986s1 |
Quadratic twists by: -11 |