Computing a lower bound for the canonical height on elliptic curves over ℚ

Authors:
John Cremona;Samir Siksek
Affiliations:
School of Mathematical Sciences, University of Nottingham, Nottingham, UK;Institute of Mathematics, University of Warwick, Coventry, UK
Venue:
ANTS'06 Proceedings of the 7th international conference on Algorithmic Number Theory
Year:
2006

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Abstract

Let E be an elliptic curve over the rationals. A crucial step in determining a Mordell-Weil basis for E is to exhibit some positive lower bound λ0 for the canonical height ĥ on non-torsion points. We give a new method for determining such a lower bound, which does not involve any searching for points.