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Computations on Modular Jacobian Surfaces

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Algorithmic Number Theory (ANTS 2002)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2369))

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Abstract

We give a method for finding rational equations of genus 2 curves whose jacobians are abelian varieties Af attached by Shimura to normalized newforms f ∈ S 2(Γ 0(N)). We present all the curves corresponding to principally polarized surfaces A f for N ≤ 500.

The first author was supported in part by DGI Grant BHA2000-0180.

The second author was supported in part by DGI Grant BFM2000-0794-C02-02.

The third author was supported in part by DGICYT Grant BFM2000-0627.

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References

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Author information

Authors and Affiliations

  1. Department de Matemàtiques, Universitat Autònoma de Barcelona, E-08193, Bellaterra, Barcelona, Spain

    Enrique González-Jiménez

  2. Escola Universitària Politècnica de Vilanova i la Geltrú, Av. Vcítor Balaguer s/n, E-08800, Vilanova i la Geltrú, Spain

    Josep González & Jordi Guàrdia

Authors
  1. Enrique González-Jiménez
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  2. Josep González
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  3. Jordi Guàrdia
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Editor information

Editors and Affiliations

  1. School of Mathematics and Statistics, F07, University of Sydney, Sydney, NSW, 2006, Australia

    Claus Fieker  & David R. Kohel  & 

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© 2002 Springer-Verlag Berlin Heidelberg

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González-Jiménez, E., González, J., Guàrdia, J. (2002). Computations on Modular Jacobian Surfaces. In: Fieker, C., Kohel, D.R. (eds) Algorithmic Number Theory. ANTS 2002. Lecture Notes in Computer Science, vol 2369. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45455-1_15

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  • DOI: https://doi.org/10.1007/3-540-45455-1_15

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-43863-2

  • Online ISBN: 978-3-540-45455-7

  • eBook Packages: Springer Book Archive

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