For any $c\ne \mathrm{\infty }$, the number of $c$-points of $f:\mathbb{C}\to \mathbb{C}$ elliptic in a cell is equal to 1;; the number of poles (counted with multiplicities). This number is called the degree of an elliptic function, and it is greater than $1$

Proof:

1. Show that if $f:\mathbb{C}\to \mathbb{C}$ is elliptic on some lattice $L$, then $f^{\prime }:\mathbb{C}\to \mathbb{C}$ is elliptic on the same lattice.
2. Observe the integral:

3. Realize that this integral also tells us about the $c$-points and poles by 15. Theorem 2.9.6 - zeros - poles.