The Canonical Height of an Algebraic Point on an Elliptic Curve

摘要

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