On group orders of retional points of elliptic curves

We consider elliptic curves without complex multiplication defined over the rationals or with complex multiplication defined over the Hilbert class field of the endomorphism ring. We examine the distribution of almost prime group orders of these curves when reduced modulo a prime ideal.Mathematics Subject Classification (2000): 11G20, 14G50, 11R45 Quaestiones Mathematicae 25 (2002), 513-52