Atkin-Lehner |
2+ 3- 11- 19+ |
Signs for the Atkin-Lehner involutions |
Class |
120384bi |
Isogeny class |
Conductor |
120384 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
50688 |
Modular degree for the optimal curve |
Δ |
-1716194304 = -1 · 210 · 36 · 112 · 19 |
Discriminant |
Eigenvalues |
2+ 3- 2 0 11- -4 2 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,96,1960] |
[a1,a2,a3,a4,a6] |
Generators |
[90:860:1] |
Generators of the group modulo torsion |
j |
131072/2299 |
j-invariant |
L |
8.6727743975407 |
L(r)(E,1)/r! |
Ω |
1.1121913205292 |
Real period |
R |
3.8989579708367 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999642508 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
120384cx1 7524e1 13376d1 |
Quadratic twists by: -4 8 -3 |