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arXiv:0901.0120 [math.NT]AbstractReferencesReviewsResources

On a theorem of Mestre and Schoof

John E. Cremona, Andrew V. Sutherland

Published 2008-12-31, updated 2009-09-08Version 3

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.

Comments: 6 pages, to appear in Journal de Th\'eorie des Nombres de Bordeaux
Journal: Journal de Th\'eorie des Nombres de Bordeaux 22 (2010), 353-358
Categories: math.NT
Subjects: 11G20
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