On the Cyclicity of the Group of imagep-Rational Points of Non-CM Elliptic Curves Original Research Article

Let E be an elliptic curve defined over image and without complex multiplication. For a prime p of good reduction, let image be the reduction of E modulo p. Assuming that certain Dedekind zeta functions have no zeros in Re(s)>3/4, we determine how often image(imagep) is a cyclic group. This result was previously obtained by J.-P. Serre using the full Generalized Riemann Hypothesis for the same Dedekind zeta functions considered by us.