LMS Journal of Computation and Mathematics

Research Article

Efficient Computation of p-Adic Heights

David Harveya1

a1 Department of Mathematics, Harvard University, 1 Oxford St, Cambridge, MA 02138, USA, dmharvey@math.harvard.edu

Abstract

We analyse and drastically improve the running time of the algorithm of Mazur, Stein and Tate for computing the canonical cyclotomic p-adic height of a point on an elliptic curve E/Q, where E has good ordinary reduction at p ≥ 5.

(Received September 12 2007)

(Accepted March 18 2008)