English

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

Number Theory 2010-01-05 v2

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.

Keywords

Cite

@article{arxiv.0912.5501,
  title  = {The number of points on an elliptic curve with square x-coordinates},
  author = {Yu Tsumura},
  journal= {arXiv preprint arXiv:0912.5501},
  year   = {2010}
}

Comments

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