  Let K be a number field, and let E be an elliptic curve over K. A famous
result by Faltings of 1983 can be reformulated for elliptic curves as follows:
if S is a set of primes of good reduction for E having density one, then the
K-isogeny class of E is determined by the function which maps a prime in S to
the size of the group of points over the residue field. In this paper, we prove
that it suffices to look at the radical of the size.
