### Defining a general curve

Hey, I am relatively new to Sage, so this question might be very simple:
I want to define a projective curve in $\mathbb{P}^2$ given by $x^3=y^3-Az^3$, where $A$ is an arbitrary non-zero element of an algebraically closed field, say C. I tried the following:

x,y,z=ProjectiveSpace(2,CC,'xyz').gens();

var('A',domain=CC);

C=Curve(x^3+y^3-A*z^3);

But I get TypeError: F (=-A*z^3 + x^3 + y^3) must be a multivariate polynomial.

Is it possible to define the curve I want in Sage? All examples of algebraic geometry in Sage I saw deal with explicitly defined curves.