Let $\wp(z)$ denote the Weierstrass $\wp$-function with respect to a lattice $\Lambda \subset \mathbb{C}$ and let $f$ be an even elliptic function with periods $\Lambda$. Prove that there exists a rational function $Q$ such that $f(z)=Q(\wp(z))$. If we write $Q(w)=p(w) / q(w)$ where $p$ and $q$ are coprime polynomials, find the degree of $f$ in terms of the degrees of the polynomials $p$ and $q$. Describe all even elliptic functions of degree two. Justify your answers. [You may use standard properties of the Weierstrass $\wp$-function.]