Computations on Modular Jacobian Surfaces

  • Enrique González-Jiménez
  • Josep González
  • Jordi Guàrdia
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2369)


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


Elliptic Curve Theta Function Abelian Variety Hyperelliptic Curve Weierstrass Point 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    H. Carayol, Sur les représentations l-adiques associées aux formes modulaires de Hilbert, Ann. Sci. École Norm. Sup. (4) 19 (1986), no. 3, 409–468.zbMATHMathSciNetGoogle Scholar
  2. 2.
    G. Frey and M. Müller, Arithmetic of modular curves and applications, Algorithmic algebra and number theory (Heidelberg, 1997), Springer, Berlin, 1999, pp. 11–48.Google Scholar
  3. 3.
    E. González-Jiménez and J. González, Modular curves of genus 2, to appear in Math. Comp.Google Scholar
  4. 4.
    J. Guàrdia, Jacobian nullwerte and algebraic equations, to appear in Journal of Algebra.Google Scholar
  5. 5.
    G. Shimura, Introduction to the arithmetic theory of automorphic functions, Publications of the Mathematical Society of Japan, No. 11. Iwanami Shoten, Publishers, Tokyo, 1971, Kanô Memorial Lectures, No. 1.zbMATHGoogle Scholar
  6. 6.
    G. Shimura, On the factors of the jacobian variety of a modular function field, J. Math. Soc. Japan 25 (1973), 523–544.zbMATHMathSciNetCrossRefGoogle Scholar
  7. 7.
    X. D. Wang, 2-dimensional simple factors of J0(N), Manuscripta Math. 87 (1995), no. 2, 179–197.zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Enrique González-Jiménez
    • 1
  • Josep González
    • 2
  • Jordi Guàrdia
    • 2
  1. 1.Department de MatemàtiquesUniversitat Autònoma de BarcelonaBellaterraSpain
  2. 2.Escola Universitària Politècnica de Vilanova i la GeltrúVilanova i la GeltrúSpain

Personalised recommendations