Atkin-Lehner |
2- 3- 11+ 13+ |
Signs for the Atkin-Lehner involutions |
Class |
89232cb |
Isogeny class |
Conductor |
89232 |
Conductor |
∏ cp |
24 |
Product of Tamagawa factors cp |
deg |
2322432 |
Modular degree for the optimal curve |
Δ |
4064650079703662592 = 224 · 33 · 11 · 138 |
Discriminant |
Eigenvalues |
2- 3- -2 4 11+ 13+ 2 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-2885224,-1884795340] |
[a1,a2,a3,a4,a6] |
Generators |
[180763658:4576180224:79507] |
Generators of the group modulo torsion |
j |
134351465835313/205590528 |
j-invariant |
L |
7.9324449030877 |
L(r)(E,1)/r! |
Ω |
0.11584960874017 |
Real period |
R |
11.411986327508 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999964051 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
11154i1 6864y1 |
Quadratic twists by: -4 13 |