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
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.
G. Frey and M. Müller, Arithmetic of modular curves and applications, Algorithmic algebra and number theory (Heidelberg, 1997), Springer, Berlin, 1999, pp. 11–48.
E. González-Jiménez and J. González, Modular curves of genus 2, to appear in Math. Comp.
J. Guàrdia, Jacobian nullwerte and algebraic equations, to appear in Journal of Algebra.
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.
G. Shimura, On the factors of the jacobian variety of a modular function field, J. Math. Soc. Japan 25 (1973), 523–544.
X. D. Wang, 2-dimensional simple factors of J0(N), Manuscripta Math. 87 (1995), no. 2, 179–197.
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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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