I can transform cubic curve without parameter using this code:
Input:
R.<x,y,z> = QQ[]
f = EllipticCurve_from_cubic(-7*x^3 + 13*x*y^2 - 5*x^2*z + 11*y^2*z - 3*x*z^2 - 2*z^3, [0,1,0])
f
Output:
Scheme morphism:
From: Projective Plane Curve over Rational Field defined by -7*x^3 + 13*x*y^2 - 5*x^2*z + 11*y^2*z - 3*x*z^2 - 2*z^3
To: Elliptic Curve defined by y^2 = x^3 + 21034*x^2 + 73922290*x + 106779857275 over Rational Field
Defn: Defined on coordinates by sending (x : y : z) to
(1/13*z : 13*y : -1/34255*x - 11/445315*z)
How to do it when there is a parameter p inside cubic like for example:
-7*x^3 + 13*x*y^2 - 5*x^2*z + 11*y^2*z - 3*x*z^2 - (2+p)*z^3
I got error when I use the same code.
