Revision history [back]

You can do this:

sage: T.<t> = FunctionField(QQ)
sage: R.<u,v> = T[]
sage: f = u^3+v^3+t
sage: h = Jacobian(f, curve=Curve(f)); h
Scheme morphism:
  From: Affine Plane Curve over Rational function field in t over Rational Field defined by u^3 + v^3 + t
  To:   Elliptic Curve defined by y^2 = x^3 + (-27/4*t^2) over Rational function field in t over Rational Field
  Defn: Defined on coordinates by sending (u, v) to
        ((-t^3)*u^4*v^4 + (-t^4)*u^4*v + (-t^4)*u*v^4 : 1/2*t^3*u^6*v^3 + (-1/2*t^3)*u^3*v^6 + (-1/2*t^4)*u^6 + 1/2*t^4*v^6 + 1/2*t^5*u^3 + (-1/2*t^5)*v^3 : t^3*u^3*v^3)