Discriminants of Complex Multiplication Fields of Elliptic Curves over Finite Fields
Florian Luca, Igor E. Shparlinski · Canadian Mathematical Bulletin · 2007
Abstract We show that, for most of the elliptic curves E over a prime finite field p of p elements, the discriminant D(E) of the quadratic number field containing the endomorphism ring of E over p is sufficiently large. We also obtain an asymptotic formula for the number of distinct quadratic number fields generated by the endomorphism rings of all elliptic curves over p.