Atkin-Lehner |
2- 7+ 89- |
Signs for the Atkin-Lehner involutions |
Class |
9968j |
Isogeny class |
Conductor |
9968 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
4608 |
Modular degree for the optimal curve |
Δ |
71450624 = 214 · 72 · 89 |
Discriminant |
Eigenvalues |
2- -2 -2 7+ 0 -4 -6 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-1464,21076] |
[a1,a2,a3,a4,a6] |
Generators |
[6:112:1] |
Generators of the group modulo torsion |
j |
84778086457/17444 |
j-invariant |
L |
1.9747883882564 |
L(r)(E,1)/r! |
Ω |
1.8911858647447 |
Real period |
R |
0.52210320124272 |
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 |
1246f1 39872bd1 89712r1 69776p1 |
Quadratic twists by: -4 8 -3 -7 |