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On a theorem of Mestre and Schoof

John E. CremonaAndrew V. Sutherland — 2010

Journal de Théorie des Nombres de Bordeaux

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 .

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