Is there a "Weierstrass form" for isogenies?

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Let $W_1$ and $W_2$ denote smooth subsets of $\mathbb{P}^2$ given by Weierstrass equations and suppose $\varphi : W_1 \rightarrow W_2$ is an isogeny. Is there a specific form that $\varphi$ can be assumed to take, a sort of "Weierstrass form" for isogenies?