Reductions of points on elliptic curves

Consider an elliptic curve E defined over a number field K, and some rational point R of infinite order. For every
prime p of K (of good reduction for E), the reduction of R modulo p is a torsion point. The order of these torsion
points gives a sequence of natural numbers that determines the curve and the point up to isomorphism. We fix some
prime number l and investigate how likely it is that the order of (R mod p) is coprime to l. In particular, we will
present some new results which are joint work with Davide Lombardo.