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Choosing the correct elliptic curve in the CM method
Authors: K. Rubin, A. SilverbergAbstract:
We give an elementary way to distinguish between the twists of an ordinary elliptic curve E over \Fp in order to identify the one with p+1-2U points, when p=U^2+\d V^2 with 2U, 2V\in \Z and E is constructed using the CM method for finding elliptic curves with a prescribed number of points. Our algorithms consist in most cases of reading off simple congruence conditions on U and V modulo 4.
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