Let E be an elliptic curve defined over a number field K. Then for every prime p of K for which E has good reduction, the point group of E modulo p is a finite abelian group on at most 2 generators. If it is cyclic, we call p a prime of cyclic reduction for E. We will answer basic questions for the set of primes of cyclic reduction of E: is this set infinite, does it have a density, and can such a density be computed explicitly from the Galois representation associated to E? This is joint work with Francesco Campagna (MPIM Bonn)