I'm trying to prove that every elliptic function of order $2$ has the form
I've got the following so far. Let $f$ be an elliptic function of order 2. Then $f$ has $2$ poles and $2$ zeroes inside the fundamental parallelogram $P$ counting with multiplicity. Choose $z_0$ s.t. $f(z_0)$ is a pole. Now $f(z)=\wp(z-z_0)$ at $z=z_0$. But now I don't really know what to do, because the multiplicity of my pole of $\wp$ doesn't necessarily match that of $f$ does it? Could someone clarify this for me, and give me a hint on how to proceed?