Atkin-Lehner |
2- 3- 11+ 13+ |
Signs for the Atkin-Lehner involutions |
Class |
89232bu |
Isogeny class |
Conductor |
89232 |
Conductor |
∏ cp |
48 |
Product of Tamagawa factors cp |
deg |
387072 |
Modular degree for the optimal curve |
Δ |
88559742976848 = 24 · 36 · 112 · 137 |
Discriminant |
Eigenvalues |
2- 3- 0 -2 11+ 13+ -2 6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-90133,-10435606] |
[a1,a2,a3,a4,a6] |
Generators |
[4426:83655:8] |
Generators of the group modulo torsion |
j |
1048576000000/1146717 |
j-invariant |
L |
6.9608541990154 |
L(r)(E,1)/r! |
Ω |
0.27555399561888 |
Real period |
R |
2.1051089528575 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.000000000135 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
22308a1 6864z1 |
Quadratic twists by: -4 13 |