On the pre-image of a point under an isogeny and Siegel's theorem
Number Theory
2010-11-02 v3
Abstract
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.
Cite
@article{arxiv.1009.0807,
title = {On the pre-image of a point under an isogeny and Siegel's theorem},
author = {Jonathan Reynolds},
journal= {arXiv preprint arXiv:1009.0807},
year = {2010}
}
Comments
8 pages