Atkin-Lehner |
2+ 3- 19- 89+ |
Signs for the Atkin-Lehner involutions |
Class |
81168z |
Isogeny class |
Conductor |
81168 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
9728 |
Modular degree for the optimal curve |
Δ |
-2191536 = -1 · 24 · 34 · 19 · 89 |
Discriminant |
Eigenvalues |
2+ 3- 1 2 1 1 -3 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-35,96] |
[a1,a2,a3,a4,a6] |
Generators |
[4:6:1] |
Generators of the group modulo torsion |
j |
-304900096/136971 |
j-invariant |
L |
9.6788804172897 |
L(r)(E,1)/r! |
Ω |
2.4323304766592 |
Real period |
R |
0.99481551843644 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000727 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
40584a1 |
Quadratic twists by: -4 |