Francesco Pappalardi :The exponent of elliptic curves over finite fields

We will review some of the results regarding upper and
lower bounds for the exponent of the groups of rational
points of an elliptic curve defined over a finite
filed. Then we will present a new lower bound that is proven
using Bugeaud estimated for size of integer solutions of
superelliptic equations.
Earlier results considered finite fields $\F_{q^m}$ where
either $q$ is fixed or $m = 1$ and $q$ is prime. Here, we let
both $q$ and $m$ vary; our estimate is explicit and does not
depend on the elliptic curve.