The order of an elliptic function is the number of poles of the function contained within a fundamental period parallelogram, counted with multiplicity. Sometimes the term ``degree'' is also used -- this usage agrees with the theory of Riemann surfaces.

This order is always a finite number; this follows from the fact that a meromorphic function can only have a finite number of poles in a compact region (such as the closure of a period parallelogram). As it turns out, the order can be any integer greater than 1.