Atkin-Lehner |
2+ 7- 89- |
Signs for the Atkin-Lehner involutions |
Class |
9968d |
Isogeny class |
Conductor |
9968 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
3328 |
Modular degree for the optimal curve |
Δ |
-4465664 = -1 · 210 · 72 · 89 |
Discriminant |
Eigenvalues |
2+ -3 3 7- -4 0 -3 -3 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,29,82] |
[a1,a2,a3,a4,a6] |
Generators |
[3:14:1] |
Generators of the group modulo torsion |
j |
2634012/4361 |
j-invariant |
L |
3.2144406047049 |
L(r)(E,1)/r! |
Ω |
1.6751940289094 |
Real period |
R |
0.47971168551705 |
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 |
4984a1 39872bn1 89712f1 69776e1 |
Quadratic twists by: -4 8 -3 -7 |