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Hyperelliptic parametrizations of \(\pmb {\mathbb {Q}}\)-curves

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Abstract

For a square-free integer N, we present a procedure to compute \(\mathbb {Q}\)-curves parametrized by rational points of the modular curve \(X_0^*(N)\) when this is hyperelliptic.

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Authors and Affiliations

  1. Departament Matemàtiques, Edif. C, Universitat Autònoma de Barcelona, 08193, Bellaterra, Catalonia, Spain

    Francesc Bars & Xavier Xarles

  2. Departament de Matemàtiques, Universitat Politècnica de Catalunya EPSEVG, Avinguda Víctor Balaguer 1, 08800, Vilanova i la Geltrú, Catalonia, Spain

    Josep González

Authors
  1. Francesc Bars
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  2. Josep González
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  3. Xavier Xarles
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Correspondence to Francesc Bars.

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Francesc Bars and Xavier Xarles are supported by MTM2016-75980-P and MDM-2014-0445. Josep González is partially supported by DGI Grant MTM2015-66180-R.

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Bars, F., González, J. & Xarles, X. Hyperelliptic parametrizations of \(\pmb {\mathbb {Q}}\)-curves. Ramanujan J 56, 103–120 (2021). https://doi.org/10.1007/s11139-020-00281-y

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  • DOI: https://doi.org/10.1007/s11139-020-00281-y

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