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The canonical height of an algebraic point on an elliptic curve.

Everest, G. and Ward, T. (2000) 'The canonical height of an algebraic point on an elliptic curve.', New York journal of mathematics., 6 . pp. 331-342.

Abstract

We use elliptic divisibility sequences to describe a method for estimating the global canonical height of an algebraic point on an elliptic curve. This method requires almost no knowledge of the number field or the curve, is simple to implement, and requires no factorization. The method is ideally suited to searching for algebraic points with small height, in connection with the elliptic Lehmer problem. The accuracy of the method is discussed.

Item Type:Article
Keywords:Canonical heights, Elliptic divisibility sequences, Elliptic curves, Number fields, Elliptic Lehmer problem
Full text:PDF - Accepted Version (312Kb)
Status:Peer-reviewed
Publisher Web site:http://www.maths.soton.ac.uk/EMIS/journals/NYJM/j/2000/6-16.html
Record Created:12 Oct 2012 12:35
Last Modified:18 Oct 2012 15:07

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