The distribution and density of cyclic groups of the reductions of an   elliptic curve over a function field
  Let $K$ be a global field of finite characteristic $p\geq2$, and let $E/K$ be a non-isotrivial elliptic curve. We give an asympotoic formula of the number of places $\nu$ for which the reduction of $E$ at $\nu$ is a cyclic group. Moreover we determine when the Dirichlet density of those places is 0. 
M\'arton Erd\'elyi
math.NT