Let E be an elliptic curve over the rationals. To get an
asymptotic to the number of primes p ≤ x
such that the reduction of E mod p has prime order
seems to be a hard question. Not so statistically
if we let E varies over a large class of elliptic curves.
We describe such a statistical result with
emphasis on the analytic aspects of the proof.
This is a joint work with Chantal David and Alina Cojocaru.