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Computing a Lower Bound for the Canonical Height on Elliptic Curves over ℚ

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Algorithmic Number Theory (ANTS 2006)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 4076))

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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 λ>0 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.

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Author information

Authors and Affiliations

  1. School of Mathematical Sciences, University of Nottingham, University Park, Nottingham, NG7 2RD, UK

    John Cremona

  2. Institute of Mathematics, University of Warwick, Coventry, CV4 7AL, UK

    Samir Siksek

Authors
  1. John Cremona
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  2. Samir Siksek
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Editor information

Editors and Affiliations

  1. Technische Universität Berlin, Germany

    Florian Hess

  2. Institut für Mathematik, MA 8–1, Technische Universität Berlin, Straße des 17. Juni 136, 10623, Berlin, Germany

    Sebastian Pauli

  3. Institut für Mathematik, Technische Universität Berlin, Fakultät II, MA 8-1, Strasse des 17. Juni 136, 10623, Berlin, Germany

    Michael Pohst

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© 2006 Springer-Verlag Berlin Heidelberg

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Cremona, J., Siksek, S. (2006). Computing a Lower Bound for the Canonical Height on Elliptic Curves over ℚ. In: Hess, F., Pauli, S., Pohst, M. (eds) Algorithmic Number Theory. ANTS 2006. Lecture Notes in Computer Science, vol 4076. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11792086_20

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  • DOI: https://doi.org/10.1007/11792086_20

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-36075-9

  • Online ISBN: 978-3-540-36076-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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