On the density of a set of primes associated to an Elliptic Curve

Abstract

For a given elliptic curve $E$ defined over the rationals, we study the density of primes $p$ satisfying $\gcd (\#E({\mathbb{F}}_p),p-1)=1$ and give a conjectural value for this density with strong heuristic evidence for most elliptic curves, in an appropriate sense.