Abstract
Let E be an elliptic curve defined over Q and without complex multiplication. For a prime p of good reduction, let Ē 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 Ē(Fp) 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.
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