Atkin-Lehner |
2+ 7- 11- 19+ |
Signs for the Atkin-Lehner involutions |
Class |
32186k |
Isogeny class |
Conductor |
32186 |
Conductor |
∏ cp |
6 |
Product of Tamagawa factors cp |
deg |
558144 |
Modular degree for the optimal curve |
Δ |
-141806823538688 = -1 · 219 · 76 · 112 · 19 |
Discriminant |
Eigenvalues |
2+ 3 -2 7- 11- 1 3 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-889708,-322790704] |
[a1,a2,a3,a4,a6] |
Generators |
[432292443:47044769974:35937] |
Generators of the group modulo torsion |
j |
-643696434148521667617/1171957219328 |
j-invariant |
L |
6.9069532907522 |
L(r)(E,1)/r! |
Ω |
0.077724442348217 |
Real period |
R |
14.81077055059 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000001 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
32186v1 |
Quadratic twists by: -11 |