Let E be an elliptic curve defined over a number field k. Canonical height on E in a certain sense measures arithmetic complexity of points of E(k). Given a real number B, it is often useful to have good bounds on the number of points of E(k) with height at most log(B), which we denote by N(B). While classical results give good bounds for a fixed elliptic curve, in general it is hard to get uniform results. This problem can be simplified if we assume the existence of a nontrivial point of prime order $\ell$ in E(k). We will present a strategy for uniformly bounding N(B) in these families of curves, following methods developed by Bombieri and Zannier and later Naccarato (in the rational case for $\ell=2$), as well as new results on how this can be generalized to arbitrary number fields.