Hostname: page-component-586b7cd67f-g8jcs Total loading time: 0 Render date: 2024-11-26T08:40:49.707Z Has data issue: false hasContentIssue false
  • English
  • Français

The modular curves X0(65) and X0(91) and rational isogeny

Published online by Cambridge University Press:  24 October 2008

M. A. Kenku
M. A. Kenku
Affiliation:
University of Ibadan, Nigeria
Get access Rights & Permissions [Opens in a new window]

Extract

Let N be an integer ≥ 1. The affine modular curve Y0(N) parameterizes isomorphism classes of pairs (E; F), where E is an elliptic curve defined over ℂ, the field of complex numbers, and F is a cyclic subgroup of order N. The compacti-fication X0(N) is an algebraic curve defined over ℚ.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 87 , Issue 1 , January 1980 , pp. 15 - 20
Copyright
Copyright © Cambridge Philosophical Society 1980

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Berkovic, B. G.Rational points on the jacobians of modular curves. (In Russian.) Math. Sbornik J. 101 (1976) (143), no. 4 (12), 542–567. Translation. Math USSR Sbornik, vol. 30 (1976), no. 4.Google Scholar
(2)Kenku, M. A.The modular curve X 0(39) and rational isogeny. Math. Proc. Cambridge Philos. Soc. 85 (1979), 21–23.CrossRefGoogle Scholar
(3)Kenku, M. A.Atkin-Lehner involutions and class-number residuality. Acta Arithmetica 33 (1977), 1–9.CrossRefGoogle Scholar
(4)Klein, F. and Fricke, R.Vorlesungen uber die Theories der elliptischen Modulfunktionen, vol. 2 (Chelsea).Google Scholar
(5)Ligozat, G. Courbes modulaires de niveau 11. In Modular functions of one variable, vol. v, 148–237. Lecture Notes in Mathematics, no. 601 (Berlin, Heidelberg, New York, Springer, 1977).Google Scholar
(6)Manin, Y.Parabolic points and zeta-functions of modular curves. Math. U.S.S.R. Izvestija 6 (1972), no. 1, 19–64.CrossRefGoogle Scholar
(7)Mazur, B.Rational isogenies of prime degree. Inventiones Math. 44 (1978), 129–162.CrossRefGoogle Scholar
(8)Newman, M.Construction and applications of a class of modular functions. Proc. London Math. Soc (3) 7 (1967), 334–350; 9 (1959), 373–387.Google Scholar
(9)Ogg, A. P.Hyperelliptic modular curves. Bull. Soc. Math. France 102 (1974), 449–462.CrossRefGoogle Scholar
(10)Ogg, A. P.Rational points on certain modular curves. Proc. Symp. Pure Math. A.M.S. Providence 24 (1973), 221–231.CrossRefGoogle Scholar
(11)Weber, H.Lehrbuch der Algebra, vol. III (Chelsea, New York).Google Scholar