New York Journal of Mathematics
Volume 6 (2000) 331-342

  

G. Everest and T. Ward

The Canonical Height of an Algebraic Point on an Elliptic Curve


Published: December 28, 2000
Keywords: Canonical heights, Elliptic divisibility sequences, Elliptic curves, Number fields, Elliptic Lehmer problem
Subject: 11G07

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.

Author information

G. Everest:
School of Mathematics, University of East Anglia, Norwich NR4 7TJ, UK.
g.everest@uea.ac.uk
http://www.mth.uea.ac.uk/~h090/

T. Ward:
School of Mathematics, University of East Anglia, Norwich NR4 7TJ, UK.
t.ward@uea.ac.uk
http://www.mth.uea.ac.uk/~h720/