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