Multiples of integral points on elliptic curves

Details Multiples of integral points on elliptic curves Multiples of integral points on elliptic curves

2008-02-19

arxiv.org/abs/0802.2651v2

Mathematics

Number Theory

Revised version, correcting a significant error

Scientific paper

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 $\Gamma\subseteq E'(\QQ)$, $\Gamma$ contains at most 6 integral points. Explicit computations for congruent number curves are included.

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