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


Author: Thotsaphon Thongjunthug
Journal: Math. Comp. 79 (2010), 2431-2449
MSC (2000): Primary 11G05; Secondary 11Y16, 11Y40
DOI: https://doi.org/10.1090/S0025-5718-10-02352-5
Published electronically: April 12, 2010
MathSciNet review: 2684374
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Abstract: Computing a lower bound for the canonical height is a crucial step in determining a Mordell-Weil basis for elliptic curves. This paper presents an algorithm for computing such a lower bound for elliptic curves over number fields without searching for points. The algorithm is illustrated by some examples.


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Additional Information

Thotsaphon Thongjunthug
Affiliation: Mathematics Institute, University of Warwick, Coventry, CV4 7AL, United Kingdom
Email: T.Thongjunthug@warwick.ac.uk

DOI: https://doi.org/10.1090/S0025-5718-10-02352-5
Keywords: Elliptic curves, canonical height, lower bound, number fields
Received by editor(s): December 19, 2009
Received by editor(s) in revised form: August 15, 2009
Published electronically: April 12, 2010
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.