Atkin-Lehner |
2- 3- 5- 11- 89+ |
Signs for the Atkin-Lehner involutions |
Class |
88110cr |
Isogeny class |
Conductor |
88110 |
Conductor |
∏ cp |
45 |
Product of Tamagawa factors cp |
deg |
172800 |
Modular degree for the optimal curve |
Δ |
2923278336000 = 215 · 36 · 53 · 11 · 89 |
Discriminant |
Eigenvalues |
2- 3- 5- 3 11- 2 -3 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-4757,-94611] |
[a1,a2,a3,a4,a6] |
Generators |
[-33:176:1] |
Generators of the group modulo torsion |
j |
16327137318409/4009984000 |
j-invariant |
L |
13.737972980668 |
L(r)(E,1)/r! |
Ω |
0.58518672844 |
Real period |
R |
0.52169380077009 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999980091 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
9790a1 |
Quadratic twists by: -3 |