The number of points on an elliptic curve with square x-coordinates

2009/12/30 by Yu Tsumura, Tsumura, Yu
Mathematics · #11G20 #14H52 #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11G20 #msc:14H52

paper · pdf · doi:10.48550/arxiv.0912.5501

2 pages, this result generalizes my old paper posted 30 Dec 2009. Comments are welcome

arxiv created 2010/01/05 · arxiv updated 2010/01/14

Abstract

Let K be a finite field. We know that a half of elements of K* is a square. So it is natural to ask how many of them appear as x-coordinate of points on an elliptic curve over K. We consider a specific class of elliptic curves over finite fields and show that a half of x-coordinate on an elliptic curve is a square. This result generalizes my old paper posted 30 Dec 2009.

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