Atkin-Lehner |
2- 3+ 11- 13+ |
Signs for the Atkin-Lehner involutions |
Class |
89232bk |
Isogeny class |
Conductor |
89232 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
80640 |
Modular degree for the optimal curve |
Δ |
236840288256 = 219 · 35 · 11 · 132 |
Discriminant |
Eigenvalues |
2- 3+ -1 -2 11- 13+ -3 -1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-1616,-8256] |
[a1,a2,a3,a4,a6] |
Generators |
[-8:64:1] |
Generators of the group modulo torsion |
j |
674636521/342144 |
j-invariant |
L |
3.4694948523612 |
L(r)(E,1)/r! |
Ω |
0.79446484387916 |
Real period |
R |
1.0917710448667 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000004364 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
11154bc1 89232ba1 |
Quadratic twists by: -4 13 |