Atkin-Lehner |
2- 3+ 19+ 89+ |
Signs for the Atkin-Lehner involutions |
Class |
81168bg |
Isogeny class |
Conductor |
81168 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
22528 |
Modular degree for the optimal curve |
Δ |
-62337024 = -1 · 212 · 32 · 19 · 89 |
Discriminant |
Eigenvalues |
2- 3+ -1 0 -3 -7 3 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-56,432] |
[a1,a2,a3,a4,a6] |
Generators |
[-4:24:1] [2:18:1] |
Generators of the group modulo torsion |
j |
-4826809/15219 |
j-invariant |
L |
8.2338016522707 |
L(r)(E,1)/r! |
Ω |
1.7285523369725 |
Real period |
R |
0.59542611731049 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.9999999999634 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
5073f1 |
Quadratic twists by: -4 |