CHOOSING THE CORRECT ELLIPTIC CURVE IN THE CM METHOD

摘要

We give an elementary way to distinguish between the twists ofan ordinary elliptic curve E over Fp in order to identify the one with p +1 — 2Upoints, when p = U~2+ dV~2with 2U, 2VE ZandEis constructed using theCM method for finding elliptic curves with a prescribed number of points. Ouralgorithms consist in mos