On a theorem of Mestre and Schoof
John E. Cremona, Andrew V. Sutherland (2010)
Journal de Théorie des Nombres de Bordeaux
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A well known theorem of Mestre and Schoof implies that the order of an elliptic curve over a prime field can be uniquely determined by computing the orders of a few points on and its quadratic twist, provided that . We extend this result to all finite fields with , and all prime fields with .