Atkin-Lehner |
2- 7+ 89- |
Signs for the Atkin-Lehner involutions |
Class |
9968h |
Isogeny class |
Conductor |
9968 |
Conductor |
∏ cp |
6 |
Product of Tamagawa factors cp |
deg |
11136 |
Modular degree for the optimal curve |
Δ |
-433313425664 = -1 · 28 · 74 · 893 |
Discriminant |
Eigenvalues |
2- -1 3 7+ 0 -4 3 -5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,356,-31684] |
[a1,a2,a3,a4,a6] |
Generators |
[1335:8722:27] |
Generators of the group modulo torsion |
j |
19436284208/1692630569 |
j-invariant |
L |
4.1069753940061 |
L(r)(E,1)/r! |
Ω |
0.44754152657149 |
Real period |
R |
1.5294578454982 |
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 |
2492c1 39872z1 89712s1 69776j1 |
Quadratic twists by: -4 8 -3 -7 |