Atkin-Lehner |
3- 11- 13- 19- |
Signs for the Atkin-Lehner involutions |
Class |
89661n |
Isogeny class |
Conductor |
89661 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
deg |
345600 |
Modular degree for the optimal curve |
Δ |
-297131750591247 = -1 · 32 · 117 · 13 · 194 |
Discriminant |
Eigenvalues |
1 3- 0 -4 11- 13- -4 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,1,-43321,-3571801] |
[a1,a2,a3,a4,a6] |
Generators |
[40369:8090687:1] |
Generators of the group modulo torsion |
j |
-5075146806625/167723127 |
j-invariant |
L |
6.4124565146337 |
L(r)(E,1)/r! |
Ω |
0.16514006759712 |
Real period |
R |
4.8538012324122 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000008804 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
8151f1 |
Quadratic twists by: -11 |