Multiples of integral points on elliptic curves
Abstract
Description
If $E$ is a minimal elliptic curve defined over $\ZZ$, we obtain a bound $C$, depending only on the global Tamagawa number of $E$, such that for any point $P\in E(\QQ)$, $nP$ is integral for at most one value of $n>C$. As a corollary, we show that if $E/\QQ$ is a fixed elliptic curve, then for all twists $E'$ of $E$ of sufficient height, and all torsion-free, rank-one subgroups $Γ\subseteq E'(\QQ)$, $Γ$ contains at most 6 integral points. Explicit computations for congruent number curves are included.
Revised version, correcting a significant error
Revised version, correcting a significant error