The canonical height of an algebraic point on an elliptic curve

Everest, G.; Ward, T.

The canonical height of an algebraic point on an elliptic curve

Everest, G.; Ward, T.

Authors

G. Everest

T. Ward

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
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
Publisher URL	http://www.maths.soton.ac.uk/EMIS/journals/NYJM/j/2000/6-16.html