Modular equations of hyperelliptic X₀(N) and an application

Takeshi Hibino; Naoki Murabayashi

Acta Arithmetica (1997)

  • Volume: 82, Issue: 3, page 279-291
  • ISSN: 0065-1036

How to cite

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Takeshi Hibino, and Naoki Murabayashi. "Modular equations of hyperelliptic X₀(N) and an application." Acta Arithmetica 82.3 (1997): 279-291. <http://eudml.org/doc/207092>.

@article{TakeshiHibino1997,
author = {Takeshi Hibino, Naoki Murabayashi},
journal = {Acta Arithmetica},
keywords = {hyperelliptic modular curve; hyperelliptic involution; computation of rational polynomials; modular invariant; number of -rational points},
language = {eng},
number = {3},
pages = {279-291},
title = {Modular equations of hyperelliptic X₀(N) and an application},
url = {http://eudml.org/doc/207092},
volume = {82},
year = {1997},
}

TY - JOUR
AU - Takeshi Hibino
AU - Naoki Murabayashi
TI - Modular equations of hyperelliptic X₀(N) and an application
JO - Acta Arithmetica
PY - 1997
VL - 82
IS - 3
SP - 279
EP - 291
LA - eng
KW - hyperelliptic modular curve; hyperelliptic involution; computation of rational polynomials; modular invariant; number of -rational points
UR - http://eudml.org/doc/207092
ER -

References

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  1. [1] A. O. L. Atkin and J. Lehner, Hecke operators on Γ₀(m), Math. Ann. 185 (1970), 134-160. 
  2. [2] N. D. Elkies, Explicit isogenies, preprint. 
  3. [3] R. Fricke, Die Elliptischen Funktionen und ihre Anwendungen, Teubner, Leipzig, 1922. Zbl48.0432.01
  4. [4] K. Hashimoto, On Brandt matrices of Eichler orders, preprint. Zbl0924.11095
  5. [5] H. Hijikata, Explicit formula of the traces of Hecke operators for Γ₀(N), J. Math. Soc. Japan 26 (1974), 56-82. Zbl0266.12009
  6. [6] M. A. Kenku and F. Momose, Automorphism groups of the modular curve X₀(N), Compositio Math. 65 (1988), 51-80. 
  7. [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. 
  8. [8] F. Momose, Rational points on the modular curves X s p l i t ( p ) , Compositio Math. 52 (1984), 115-137. 
  9. [9] N. Murabayashi, On normal forms of modular curves of genus 2, Osaka J. Math. 29 (1992), 405-418. Zbl0774.14025
  10. [10] A. Ogg, Hyperelliptic modular curves, Bull. Soc. Math. France 102 (1974), 449-462. Zbl0314.10018
  11. [11] A. Pizer, An algorithm for computing modular forms on Γ₀(N), J. Algebra 64 (1980), 340-390. Zbl0433.10012
  12. [12] G. Shimura, Introduction to the Arithmetic Theory of Automorphic Functions, Iwanami Shoten and Princeton Univ. Press, 1971. Zbl0221.10029
  13. [13] M. Shimura, Defining equations of modular curves X₀(N), Tokyo J. Math. 18 (1995), 443-456. Zbl0865.11052
  14. [14] M. Yamauchi, On the traces of Hecke operators for a normalizer of Γ₀(N), J. Math. Kyoto Univ. 13 (1973), 403-411. Zbl0267.10038

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