The canonical height of an algebraic point on an elliptic curve

Everest, G.; Ward, T.

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.

Citation

Everest, G., & Ward, T. (2000). The canonical height of an algebraic point on an elliptic curve. New York journal of mathematics, 6, 331-342

• Journal Article Type: Article
• Publication Date: Dec 1, 2000
• Deposit Date: Oct 12, 2012
• Publicly Available Date: Oct 18, 2012
• Journal: New York journal of mathematics
• Electronic ISSN: 1076-9803
• Publisher: State University of New York at Albany
• Peer Reviewed: Peer Reviewed
• Volume: 6
• Pages: 331-342
• Keywords: Canonical heights, Elliptic divisibility sequences, Elliptic curves, Number fields, Elliptic Lehmer problem
• Public URL: https://durham-repository.worktribe.com/output/1495295
• Publisher URL: http://www.maths.soton.ac.uk/EMIS/journals/NYJM/j/2000/6-16.html