Atkin-Lehner |
2- 3- 13+ 89+ |
Signs for the Atkin-Lehner involutions |
Class |
83304p |
Isogeny class |
Conductor |
83304 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
537600 |
Modular degree for the optimal curve |
Δ |
-1498582081361664 = -1 · 28 · 311 · 135 · 89 |
Discriminant |
Eigenvalues |
2- 3- -1 -1 -5 13+ 0 -1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-524703,-146303134] |
[a1,a2,a3,a4,a6] |
Generators |
[893:9862:1] |
Generators of the group modulo torsion |
j |
-85604552312875216/8029953711 |
j-invariant |
L |
4.4788330691426 |
L(r)(E,1)/r! |
Ω |
0.088692874013604 |
Real period |
R |
6.3122786331518 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000001678 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
27768a1 |
Quadratic twists by: -3 |