Location of Small Points on an Elliptic Curve by an Equidistribution Argument

Let E be an elliptic curve defined over a number field K without complex multiplication. If Gamma subset of E ((K) over bar is a subgroup of finite rank, a very special case of a conjecture of Remond predicts that points of small height in E(K(Gamma)) lie in the division group of Gamma. Using an equidistribution argument, we will show that this conjecture is true for groups of rank arbitarily large.