Atkin-Lehner |
2- 3- 5- 11- 89- |
Signs for the Atkin-Lehner involutions |
Class |
88110cu |
Isogeny class |
Conductor |
88110 |
Conductor |
∏ cp |
780 |
Product of Tamagawa factors cp |
deg |
698880 |
Modular degree for the optimal curve |
Δ |
-6632187724800000 = -1 · 213 · 37 · 55 · 113 · 89 |
Discriminant |
Eigenvalues |
2- 3- 5- -3 11- -6 -8 -3 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-28382,4335981] |
[a1,a2,a3,a4,a6] |
Generators |
[-109:-2421:1] [-199:1539:1] |
Generators of the group modulo torsion |
j |
-3468253438176409/9097651200000 |
j-invariant |
L |
15.756461556703 |
L(r)(E,1)/r! |
Ω |
0.37249348299897 |
Real period |
R |
0.054230725264126 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000083 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
29370a1 |
Quadratic twists by: -3 |