$f'(z) = \wp(z)$, Weierstrass $\wp$ function

Question

Let $\wp$ be the Weierstrass elliptic function. Is there a meromorphic function $f$ from $\mathbb{C}/L$ such that $f'(z) = \wp(z)$? Here $L$ is the usual lattice $(m\omega_1 + n\omega_2 | m,n \in \mathbb{Z})$.

As a hint I am given "What would the poles of $f$ look like?" but I have no idea how to think on this.

Answer 1

This is the negative of the Weierstrass zeta function. It has simple poles with residue 1 at each point of the lattice. It is not an elliptic function.