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First off, the method is called .rational_parameterization() not just .parameterization(), but nevertheless it gives an error.
You can try to start with
P2.<x,y,z> = ProjectiveSpace(QQ, 2)
f = (x^2+y^2)^4 - 3*(x^2+y^2)^2 - 2*(x^2-y^2)
C = Curve( f.homogenize(z) )
and then proceed as in this answer.
