English

On a theorem of Mestre and Schoof

Number Theory 2012-06-26 v3

Abstract

A well known theorem of Mestre and Schoof implies that the order of an elliptic curve E over a prime field F_q can be uniquely determined by computing the orders of a few points on E and its quadratic twist, provided that q > 229. We extend this result to all finite fields with q > 49, and all prime fields with q > 29.

Keywords

Cite

@article{arxiv.0901.0120,
  title  = {On a theorem of Mestre and Schoof},
  author = {John E. Cremona and Andrew V. Sutherland},
  journal= {arXiv preprint arXiv:0901.0120},
  year   = {2012}
}

Comments

6 pages, to appear in Journal de Th\'eorie des Nombres de Bordeaux