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On the ubiquity of trivial torsion on elliptic curves

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Abstract

The purpose of this paper is to give a down-to-earth proof of the well-known fact that a randomly chosen elliptic curve over the rationals is most likely to have trivial torsion.

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Authors and Affiliations

  1. Departamento de Matemáticas, Universidad Autoónoma de Madrid and Instituto de Ciencias Matemáticas (CSIC-UAM-UC3M-UCM), 28049, Madrid, Spain

    Enrique González-Jiménez

  2. Departamento de Álgebra, Universidad de Sevilla, P.O. 1160, 41080, Sevilla, Spain

    José M. Tornero

Authors
  1. Enrique González-Jiménez
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  2. José M. Tornero
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Corresponding author

Correspondence to José M. Tornero.

Additional information

The first author was supported in part by grants MTM 2009-07291 (Ministerio de Educación y Ciencia, Spain) and CCG08-UAM/ESP-3906 (Universidad Autonóma de Madrid-Comunidad de Madrid, Spain). The second author was partially supported by grants FQM–218 and P08–FQM–03894 (Junta de Andalucía) and MTM 2007–66929 (Ministerio de Educación y Ciencia, Spain).

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González-Jiménez, E., Tornero, J.M. On the ubiquity of trivial torsion on elliptic curves. Arch. Math. 95, 135–141 (2010). https://doi.org/10.1007/s00013-010-0145-x

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  • DOI: https://doi.org/10.1007/s00013-010-0145-x

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