Type: Article

Pseudoprime reductions of elliptic curves

Alina Carmen Cojocaru; Florian Luca; Igor E. Shparlinski;

Abstract:

Let b >= 2 be an integer and let E/Q 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).