How to find the ideal of a rationally parametrized projective curve using computer software?

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If I have a curve given by $[X_0^3,X_0X_1^2,X_1^3]\in\mathbb{P}^2$ where $[X_0,X_1]\in \mathbb{P}^1$, then I find that the curve is the zero locus of the polynomial $Z_0Z_2^2-Z_1^3$. How can I find this polynomial using computer software, such as Sage or Singular?