Atkin-Lehner |
11+ 19+ 43+ |
Signs for the Atkin-Lehner involutions |
Class |
8987a |
Isogeny class |
Conductor |
8987 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
992 |
Modular degree for the optimal curve |
Δ |
-7342379 = -1 · 11 · 192 · 432 |
Discriminant |
Eigenvalues |
0 -1 -1 2 11+ 0 4 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,1,39,-105] |
[a1,a2,a3,a4,a6] |
Generators |
[7:21:1] |
Generators of the group modulo torsion |
j |
6393430016/7342379 |
j-invariant |
L |
2.5711791001785 |
L(r)(E,1)/r! |
Ω |
1.2662330165805 |
Real period |
R |
0.50764335365424 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
80883l1 98857e1 |
Quadratic twists by: -3 -11 |