order of an elliptic function

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 thetheory 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, theorder can be any integer greater than 1.