Computing divisors on an elliptic surface from a Weierstrass equation

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Let $\mathcal{E} \rightarrow \mathbb{P}^1$ be a minimal elliptic surface over the projective line and let $\mathcal{E}_w$ be a Weierstrass model of $\mathcal{E}$. If we only know the equation for $\mathcal{E}_w$, is there a way to take a function $f$ on $\mathcal{E}_w$ and compute its divisor as a function on $\mathcal{E}$?