Pseudoprime reductions of elliptic curves

Let b ≥ 2 be an integer and let E / be a fixed elliptic curve. In this paper, we estimate the number of primes p ≤ x such that the number of points n E ( p ) on the reduction of E modulo p is a base b prime or pseudoprime. In particular, we improve previously known bounds which applied only to prime values of n E ( p ).