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The characterization of elliptic curves over finite fields

Part of: Curves Finite geometry and special incidence structures

Published online by Cambridge University Press:  09 April 2009

J. W. P. Hirschfeld  and
J. F. Voloch
J. W. P. Hirschfeld
Affiliation:
Mathematics Division, University of SussexBrighton BN1 9QH, United Kingdom
J. F. Voloch
Affiliation:
I.M.P.A., Est. D. Castorina 110, Rio de Janeiro 22460, Brazil
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Abstract

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In a finite Desarguesian plane of odd order, it was shown by Segre thirty years ago that a set of maximum size with at most two points on a line is a conic. Here, in a plane of odd or even order, sufficient conditions are given for a set with at most three points on a line to be a cubic curve. The case of an elliptic curve is of particular interest.

MSC classification

Secondary: 51E15: Affine and projective planes 14H25: Arithmetic ground fields
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 45 , Issue 2 , October 1988 , pp. 275 - 286
Copyright
Copyright © Australian Mathematical Society 1988

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