Modular equations of hyperelliptic X₀(N) and an application
Takeshi Hibino ; Naoki Murabayashi
Acta Arithmetica, Tome 80 (1997), p. 279-291 / Harvested from The Polish Digital Mathematics Library
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Publié le : 1997-01-01
EUDML-ID : urn:eudml:doc:207092 
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     author = {Takeshi Hibino and Naoki Murabayashi},
     title = {Modular equations of hyperelliptic X0(N) and an application},
     journal = {Acta Arithmetica},
     volume = {80},
     year = {1997},
     pages = {279-291},
     zbl = {0894.11019},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-aav82i3p279bwm}
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Takeshi Hibino; Naoki Murabayashi. Modular equations of hyperelliptic X₀(N) and an application. Acta Arithmetica, Tome 80 (1997) pp. 279-291. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-aav82i3p279bwm/

[000] [1] A. O. L. Atkin and J. Lehner, Hecke operators on Γ₀(m), Math. Ann. 185 (1970), 134-160.

[001] [2] N. D. Elkies, Explicit isogenies, preprint.

[002] [3] R. Fricke, Die Elliptischen Funktionen und ihre Anwendungen, Teubner, Leipzig, 1922. | Zbl 48.0432.01

[003] [4] K. Hashimoto, On Brandt matrices of Eichler orders, preprint. | Zbl 0924.11095

[004] [5] H. Hijikata, Explicit formula of the traces of Hecke operators for Γ₀(N), J. Math. Soc. Japan 26 (1974), 56-82. | Zbl 0266.12009

[005] [6] M. A. Kenku and F. Momose, Automorphism groups of the modular curve X₀(N), Compositio Math. 65 (1988), 51-80.

[006] [7] B. Mazur, Rational points on modular curves, in: Modular Functions of One Variable V (Bonn, 1976), Lecture Notes in Math. 601, Springer, Berlin, 1977, 107-148.

[007] [8] F. Momose, Rational points on the modular curves Xsplit(p), Compositio Math. 52 (1984), 115-137.

[008] [9] N. Murabayashi, On normal forms of modular curves of genus 2, Osaka J. Math. 29 (1992), 405-418. | Zbl 0774.14025

[009] [10] A. Ogg, Hyperelliptic modular curves, Bull. Soc. Math. France 102 (1974), 449-462. | Zbl 0314.10018

[010] [11] A. Pizer, An algorithm for computing modular forms on Γ₀(N), J. Algebra 64 (1980), 340-390. | Zbl 0433.10012

[011] [12] G. Shimura, Introduction to the Arithmetic Theory of Automorphic Functions, Iwanami Shoten and Princeton Univ. Press, 1971. | Zbl 0221.10029

[012] [13] M. Shimura, Defining equations of modular curves X₀(N), Tokyo J. Math. 18 (1995), 443-456. | Zbl 0865.11052

[013] [14] M. Yamauchi, On the traces of Hecke operators for a normalizer of Γ₀(N), J. Math. Kyoto Univ. 13 (1973), 403-411. | Zbl 0267.10038