Atkin-Lehner |
2+ 3+ 19+ 89- |
Signs for the Atkin-Lehner involutions |
Class |
81168f |
Isogeny class |
Conductor |
81168 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
304128 |
Modular degree for the optimal curve |
Δ |
-332204738448384 = -1 · 210 · 312 · 193 · 89 |
Discriminant |
Eigenvalues |
2+ 3+ -1 4 3 1 -7 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-27856,-1983536] |
[a1,a2,a3,a4,a6] |
j |
-2334509294836036/324418689891 |
j-invariant |
L |
1.4668627388047 |
L(r)(E,1)/r! |
Ω |
0.18335784107504 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
40584j1 |
Quadratic twists by: -4 |