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≥2, and let E/K be a non-isotrivial elliptic curve. We give an asymptotic formula of the number of places ν for which the reduction of E at ν is a cyclic group. Moreover we determine when the Dirichlet density of those places is 0.