Atkin-Lehner |
3+ 11+ 101+ |
Signs for the Atkin-Lehner involutions |
Class |
9999a |
Isogeny class |
Conductor |
9999 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
8640 |
Modular degree for the optimal curve |
Δ |
44357793777 = 33 · 115 · 1012 |
Discriminant |
Eigenvalues |
-1 3+ 0 2 11+ -2 -6 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-9965,385220] |
[a1,a2,a3,a4,a6] |
Generators |
[-44:880:1] |
Generators of the group modulo torsion |
j |
4052761047637875/1642881251 |
j-invariant |
L |
2.7682265599138 |
L(r)(E,1)/r! |
Ω |
1.1193546931511 |
Real period |
R |
2.473055749756 |
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 |
9999c1 109989c1 |
Quadratic twists by: -3 -11 |