Atkin-Lehner |
3+ 11- 13- 23+ |
Signs for the Atkin-Lehner involutions |
Class |
9867g |
Isogeny class |
Conductor |
9867 |
Conductor |
∏ cp |
6 |
Product of Tamagawa factors cp |
deg |
137280 |
Modular degree for the optimal curve |
Δ |
1011583801834263801 = 326 · 113 · 13 · 23 |
Discriminant |
Eigenvalues |
-1 3+ 2 -2 11- 13- 2 6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,1,-539732,-144971764] |
[a1,a2,a3,a4,a6] |
Generators |
[626868:3521159:729] |
Generators of the group modulo torsion |
j |
17388345671060487020353/1011583801834263801 |
j-invariant |
L |
2.6384604355254 |
L(r)(E,1)/r! |
Ω |
0.17677875558325 |
Real period |
R |
9.9501414515571 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
29601c1 108537a1 128271a1 |
Quadratic twists by: -3 -11 13 |