Atkin-Lehner |
2- 3- 19- 89+ |
Signs for the Atkin-Lehner involutions |
Class |
81168ck |
Isogeny class |
Conductor |
81168 |
Conductor |
∏ cp |
72 |
Product of Tamagawa factors cp |
deg |
110592 |
Modular degree for the optimal curve |
Δ |
-1822796918784 = -1 · 212 · 36 · 193 · 89 |
Discriminant |
Eigenvalues |
2- 3- -1 -2 -1 -1 3 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-10496,415476] |
[a1,a2,a3,a4,a6] |
Generators |
[58:-72:1] [-62:912:1] |
Generators of the group modulo torsion |
j |
-31223142183169/445018779 |
j-invariant |
L |
11.865552939082 |
L(r)(E,1)/r! |
Ω |
0.83773937118096 |
Real period |
R |
0.19671911342033 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000007 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
5073b1 |
Quadratic twists by: -4 |