| Hosted by CoCalc | Download

Points on y2=x(x−3)(x+4)y^2 = x(x-3)(x+4).

expand(x*(x-3)*(x+4))
x^3 + x^2 - 12*x 
E = EllipticCurve([0,1,0,-12,0]); show(E)
y2=x3+x2−12x\displaystyle y^2 = x^{3} + x^{2} - 12 x 
E.conductor()
168 
E.rank()
0 
E.cremona_label()
'168a2' 
E.integral_points()
[(-4 : 0 : 1), (0 : 0 : 1), (3 : 0 : 1)] 
E.torsion_points()
[(-4 : 0 : 1), (0 : 0 : 1), (0 : 1 : 0), (3 : 0 : 1)]