Abstract
In this paper we investigate abelian varietyA f which is derived from a newformf ∈ S 2(Г0(N)) an is ℚ-simple factors ofJac(X 0 (N)). We will develop algorithms for computing the period matrix ofA f and for determing whenA f is principally polarized. IfA f is 2-dimensional principally polarized, we give an algorithm for computing the associated hyperelliptic curveC withJac(C)≊A f.
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References
[Bol] O. Bolza:Darstellung der rational ganzen Invarianten der Binärform sechsten Grades durch die Nullwerthe der zugehörigen θ-Function Math. Ann. 30 (1887)
[Cas] J.W.S. Cassels:The Mordell-Weil group of curves of genus 2 inArithmetic and Geometry, Progress in Math. Vol. 35 (1991)
[Cre1] J. E. Cremona:Abelian varieties with extra twist, cusp forms, and elliptic curves over imaginary quadratic fields J. London Math. Soc. 45 (1992) p404–416
[Cre2] J. E. Cremona:Algorithms for modular elliptic curves Cambridge University Press (1992)
[GH] P. Griffiths and J. Harris:Principles of algebraic geometry John Wiley & Sons, Inc. (1978)
[Hab] K. Haberland:Perioden von Modulformen einer Variabler und Gruppencohomologie I,II,III Math. Nachr. 112 (1983) p245–315
[Hid] H. Hida:Congruences of cusp forms and special values of their zeta functions Invent. Math. 63 (1981) p225–261
[Igu] J. I. Igusa:Arithmetic variety of moduli of genus two Ann. Math. 72 (1960), p612–649
[LB] H. Lange and Ch. Birkenkake:Complex abelian varieties Springer Verlag (1992)
[Liu] Q. Liu:Modèles minimaux des courbes de genre deux J. Reine Angew. Math. 453 (1994)
[Map]Maple V Language Reference Manual Springer Verlag (1992)
[Mes] J.-F. Mestre:Construction de courbes de genre 2 à partir de leurs modules in:Effective metheods in algebraic geometry, Progress in Math. Vol. 94 (1983)
[Mum] D. Mumford:Thata Lectures on Theta I, II Verlag Birkhäuser (1983)
[Shi] G. Shimura:On the factors of the jacobian variety of a modular function field J. Math. Soc. Japan Vol. 25 (1973)
[Spa] A.-M. Spallek:Kurven vom Geschlecht 2 und ihre Anwendung in Public-Key-Kryptosystemen Dissertation, Preprint IEM No. 18 (1994)
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Wang, X. 2-dimensional simple factors ofJ 0(N). Manuscripta Math 87, 179–197 (1995). https://doi.org/10.1007/BF02570470
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DOI: https://doi.org/10.1007/BF02570470