Atkin-Lehner |
2- 3- 11- 19+ |
Signs for the Atkin-Lehner involutions |
Class |
120384dg |
Isogeny class |
Conductor |
120384 |
Conductor |
∏ cp |
48 |
Product of Tamagawa factors cp |
deg |
276480 |
Modular degree for the optimal curve |
Δ |
-146796395986944 = -1 · 215 · 311 · 113 · 19 |
Discriminant |
Eigenvalues |
2- 3- -1 -2 11- -4 3 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-6348,614576] |
[a1,a2,a3,a4,a6] |
Generators |
[46:-648:1] [-35:891:1] |
Generators of the group modulo torsion |
j |
-1184287112/6145227 |
j-invariant |
L |
10.902999600725 |
L(r)(E,1)/r! |
Ω |
0.50205179958999 |
Real period |
R |
0.4524350377541 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000004979 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
120384cw1 60192d1 40128be1 |
Quadratic twists by: -4 8 -3 |