Atkin-Lehner |
2- 7- 89+ |
Signs for the Atkin-Lehner involutions |
Class |
69776n |
Isogeny class |
Conductor |
69776 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
442368 |
Modular degree for the optimal curve |
Δ |
-537990045630464 = -1 · 220 · 78 · 89 |
Discriminant |
Eigenvalues |
2- -1 -1 7- 0 -2 3 -5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-1295576,568033264] |
[a1,a2,a3,a4,a6] |
Generators |
[642:686:1] |
Generators of the group modulo torsion |
j |
-499073536793161/1116416 |
j-invariant |
L |
3.8625030806586 |
L(r)(E,1)/r! |
Ω |
0.44859321789957 |
Real period |
R |
1.0762821767397 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.000000000105 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
8722d1 9968e1 |
Quadratic twists by: -4 -7 |