Hostname: page-component-7c8c6479df-ph5wq Total loading time: 0 Render date: 2024-03-28T16:37:45.927Z Has data issue: false hasContentIssue false

The modular curve X0(39) and rational isogeny

Published online by Cambridge University Press:  24 October 2008

M. A. Kenku
Affiliation:
University of Ibadan

Extract

Recently (3) Mazur proved that if N is a prime number such that some elliptic curve E over Q admits a Q-rational isogeny then N is one of 2, 3, 5, 7, 11, 13, 17, 19, 37, 43, 67 or 163.

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1979

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)Birch, B. J. and Kuyk, W.Modular functions of one variable, 1st ed., vol. IV (Lecture Notes in Mathematics, no. 476; Berlin, Heidelberg, New York, Springer, 1973).Google Scholar
(2)Kenku, M. A.Atkin-Lehner involutions and class number residuality. Acta Arith. 33 (1977), 19.CrossRefGoogle Scholar
(3)Mazur, B.Rational isogenies of prime degree. Inventiones Math. 44 (1978), 129162.CrossRefGoogle Scholar
(4)Newman, M.Construction and application of a class of modular functions. Proc. London Math. Soc. (3) 7 1957, 334350;CrossRefGoogle Scholar
(4)Newman, M.Construction and application of a class of modular functions. Proc. London Math. Soc. (3) 9 (1959), 373387.CrossRefGoogle Scholar
(5)Ogg, A. P.Rational points on certain elliptic modular curves. Proc. Symp. Pure Math. AMS Providence, 24 (1973), 221231.CrossRefGoogle Scholar