Elasticity of Orders with Prime Conductor

Let $R$ be an order in a number field whose conductor ideal $P:=(R:\bar{R})$ is prime in the ring of integers $\bar{R}$. In this paper, we explore the factorization properties of such orders. Most notably, we give a complete characterization of the elasticity of $R$ in terms of its class group. We conclude with an application to the computation of class groups of certain orders.