Hyperelliptic modular curves

Andrew P. Ogg

Bulletin de la Société Mathématique de France (1974)

  • Volume: 102, page 449-462
  • ISSN: 0037-9484

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Ogg, Andrew P.. "Hyperelliptic modular curves." Bulletin de la Société Mathématique de France 102 (1974): 449-462. <http://eudml.org/doc/87238>.

@article{Ogg1974,
author = {Ogg, Andrew P.},
journal = {Bulletin de la Société Mathématique de France},
language = {eng},
pages = {449-462},
publisher = {Société mathématique de France},
title = {Hyperelliptic modular curves},
url = {http://eudml.org/doc/87238},
volume = {102},
year = {1974},
}

TY - JOUR
AU - Ogg, Andrew P.
TI - Hyperelliptic modular curves
JO - Bulletin de la Société Mathématique de France
PY - 1974
PB - Société mathématique de France
VL - 102
SP - 449
EP - 462
LA - eng
UR - http://eudml.org/doc/87238
ER -

References

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  1. [1] ATKIN (A. O. L.). — Weierstrass points at cusps of Γ0 (n), Annals of Math., t. 85, 1967, p. 42-45. Zbl0145.31904MR36 #1646
  2. [2] ATKIN (A. O. L.) and LEHNER (J.). — Hecke operators on Γ0 (m), Math. Annalen, t. 185, 1970, p. 134-160. Zbl0177.34901MR42 #3022
  3. [3] HECKE (E.). — Mathematische Werke. — Göttingen, Vandenhoeck und Ruprecht, 1959. Zbl0092.00102MR21 #3303
  4. [4] LARCHER (H.). — Weierstrass points at the cups of Γ0 (16 p) and hyperellipticity of Γ0 (n), Canadian J. Math., t. 23, 1971, p. 960-968. Zbl0215.34902MR44 #6953
  5. [5] LEHNER (J.) and NEWMAN (M.). — Weierstrass points of Γ0 (n), Annals of Math., t. 79, 1964, p. 360-368. Zbl0124.29203MR28 #5045
  6. [6] MAZUR (B.). — Modular curves and the Eisenstein ideal (In preparation). Zbl0394.14008
  7. [7] MAZUR (B.) and SWINNERTON-DYER (P.). — Arithmetic of Weil curves, Invent. Math., t. 25, 1974, p. 1-61. Zbl0281.14016MR50 #7152
  8. [8] NEWMAN (M.). — Construction and applications of a class of modular functions, Proc. London math. Soc., t. 7, 1957, p. 334-350. Zbl0097.28701MR19,953c
  9. [9] NEWMAN (M.). — Conjugacy, genus, and class numbers, Math. Annalen, t. 196, 1972, p. 198-217. Zbl0221.10030MR47 #135
  10. [10] OGG (A.). — Rational points on certain elliptic modular curves ; “Analytic number theory”, p. 221-231. — Providence, American mathematical Society, 1973 (Proceedings of Symposia in pure Mathematics, 24). Zbl0273.14008MR49 #2743
  11. [11] OGG (A.). — Diophantine equations and modular forms, Talk at the November 1973 meeting of the AMS in Tucson, to appear in the Bulletin AMS. Zbl0316.14012
  12. [12] SCHOENEBERG (B.). — Über die Weierstrasspunkte in den Körpern der elliptischen Modulfunktionen, Abh. Math. Sem. Hamburg, t. 17, 1951, p. 104-111. Zbl0042.31902MR13,439c
  13. [13] SHIMURA (G.). — Introduction to the arithmetic theory of automorphic functions. — Tokyo and Princeton, Shoten, 1971. Zbl0221.10029
  14. [14] WADA (H.). — A table of Hecke operators, Proc. Japan Acad., t. 49, 1973, p. 380-384. Zbl0273.10019MR52 #283

Citations in EuDML Documents

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  1. Jean-Francis Michon, Courbes de Shimura hyperelliptiques
  2. Andrew P. Ogg, Automorphismes de courbes modulaires
  3. Yuji Hasegawa, Hyperelliptic modular curves X * 0 ( N )
  4. Yuji Hasegawa, Ki-ichiro Hashimoto, Hyperelliptic modular curves X₀*(N) with square-free levels
  5. Barry Mazur, Jean-Pierre Serre, Points rationnels des courbes modulaires X 0 ( N )
  6. B. Morlaye, Points rationnels sur 𝐐 de certaines courbes modulaires
  7. Kuang-Yen Shih, P-division points on certain elliptic curves
  8. Yuji Hasegawa, Mahoro Shimura, Trigonal modular curves
  9. Takeshi Hibino, Naoki Murabayashi, Modular equations of hyperelliptic X₀(N) and an application
  10. Sheldon Kamienny, Torsion points on elliptic curves over all quadratic fields. II

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