  Consider a rational point on an elliptic curve under an isogeny. Suppose that
the action of Galois partitions the set of its pre-images into n orbits. It is
shown that all such points above a certain height have their denominator
divisible by at least n distinct primes. This generalizes Siegel's theorem and
more recent results of Everest et al. For multiplication by a prime l, it is
shown that if n>1 then either the point is l times a rational point or the
elliptic curve emits a rational l-isogeny.
