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Construction of elliptic curves with cyclic groups over prime fields

Published online by Cambridge University Press:  17 April 2009

Naoya Nakazawa
Naoya Nakazawa
Affiliation:
Graduate school of Science, Osaka Prefecture University, 1–1 Gakuen-cho, Sakai, Osaka 599–8531, Japan e-mail: nao-nkzw@smail.plala.or.jp
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The purpose of this article is to construct families of elliptic curves E over finite fields F so that the groups of F-rational points of E are cyclic, by using a representation of the modular invariant function by a generator of a modular function field associated with the modular group Γ0(N), where N = 5, 7 or 13.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 73 , Issue 2 , April 2006 , pp. 245 - 254
Copyright
Copyright © Australian Mathematical Society 2006

References

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