ArticleOriginal scientific text

Title

Hyperelliptic modular curves X0(N)

Authors 1

Affiliations

  1. Department of Mathematics, Waseda University, 3-4-1, Okubo Shinjuku-ku, Tokyo 169, Japan

Bibliography

  1. A. O. L. Atkin and J. Lehner, Hecke operators on Γ0(m), Math. Ann. 185 (1970), 134-160.
  2. A. O. L. Atkin and D. J. Tingley, Numerical tables on elliptic curves, in: Modular Functions of One Variable IV, B. Birch and W. Kuyk (eds.), Lecture Notes in Math. 476, Springer, Berlin, 1975, 74-144.
  3. P. Deligne et M. Rapoport, Les schémas de modules de courbes elliptiques, in: Modular Functions of One Variable II, P. Deligne and W. Kuyk (eds.), Lecture Notes in Math. 349, Springer, Berlin, 1973, 143-316.
  4. R. Fricke, Die Elliptischen Funktionen und ihre Anwendungen, Teubner, Leipzig and Berlin, 1916.
  5. Y. Hasegawa, Table of quotient curves of modular curves X0(N) with genus 2, Proc. Japan Acad. Ser. A 71 (1995), 235-239.
  6. Y. Hasegawa, Modular abelian surfaces and hyperelliptic curves of genus two, preprint.
  7. Y. Hasegawa and K. Hashimoto, Hyperelliptic modular curves X0(N) with square-free levels, Acta Arith. 77 (1996), 179-193.
  8. H. Hijikata, Explicit formula of the traces of Hecke operators for Γ0(N), J. Math. Soc. Japan 26 (1974), 56-82.
  9. P. G. Kluit, Hecke operators on Γ*(N) and their traces, Dissertation of Vrije Universiteit, Amsterdam, 1979.
  10. J. Lehner and M. Newman, Weierstrass points of Γ0(N), Ann. of Math. 79 (1964), 360-368.
  11. N. Murabayashi, On normal forms of modular curves of genus 2, Osaka J. Math. 29 (1992), 405-418.
  12. A. P. Ogg, Hyperelliptic modular curves, Bull. Soc. Math. France 102 (1974), 449-462.
  13. M. Yamauchi, On the traces of Hecke operators for a normalizer of Γ0(N), J. Math. Kyoto Univ. 13 (1973), 403-411.
Pages:
369-385
Main language of publication
English
Received
1996-11-22
Accepted
1997-02-21
Published
1997
Exact and natural sciences