On the denominators of rational points on elliptic curves

Everest, Graham, Reynolds, Jonathan and Stevens, Shaun (2007) On the denominators of rational points on elliptic curves. Bulletin of the London Mathematical Society, 39 (5). pp. 762-770. ISSN 0024-6093

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Abstract

We consider the structure of rational points on elliptic curves in Weierstrass form. Let x(P)= AP/BP2 denote the x-coordinate of the rational point P then we consider when BP can be a prime power. Using Faltings' Theorem we show that for a fixed power greater than 1, there are only finitely many rational points. Where descent via an isogeny is possible we show, with no restrictions on the power, that there are only finitely many rational points, these points are bounded in number in an explicit fashion, and that they are effectively computable.

Item Type:	Article
Faculty \ School:	Faculty of Science > School of Mathematics (former - to 2024)
UEA Research Groups:	Faculty of Science > Research Groups > Algebra and Combinatorics (former - to 2024) Faculty of Science > Research Groups > Number Theory (former - to 2017) Faculty of Science > Research Groups > Algebra, Logic & Number Theory
Related URLs:	http://arxiv.org/abs/math.NT/0606003 http://www.ams.org/mathscinet-getitem?mr...
Depositing User:	Vishal Gautam
Date Deposited:	18 Mar 2011 14:44
Last Modified:	13 Nov 2024 00:34
URI:	https://ueaeprints.uea.ac.uk/id/eprint/20913
DOI:	10.1112/blms/bdm061

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