Atkin-Lehner |
2- 41+ 53- |
Signs for the Atkin-Lehner involutions |
Class |
8692a |
Isogeny class |
Conductor |
8692 |
Conductor |
∏ cp |
18 |
Product of Tamagawa factors cp |
deg |
3744 |
Modular degree for the optimal curve |
Δ |
-64067132672 = -1 · 28 · 412 · 533 |
Discriminant |
Eigenvalues |
2- 1 0 2 0 -1 3 -1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-1268,20804] |
[a1,a2,a3,a4,a6] |
Generators |
[20:62:1] |
Generators of the group modulo torsion |
j |
-881422162000/250262237 |
j-invariant |
L |
5.2816641353492 |
L(r)(E,1)/r! |
Ω |
1.0474578854253 |
Real period |
R |
2.521182096598 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
3 |
Number of elements in the torsion subgroup |
Twists |
34768c1 78228g1 |
Quadratic twists by: -4 -3 |