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6

MOC
2010

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Choosing the correct elliptic curve in the CM method

12 years 11 months ago

Choosing the correct elliptic curve in the CM method

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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 = U2 + dV 2 with 2U, 2V 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.

Karl Rubin, Alice Silverberg

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Added	20 May 2011
Updated	20 May 2011
Type	Journal
Year	2010
Where	MOC
Authors	Karl Rubin, Alice Silverberg

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