Resumen de Discriminants of Complex Multiplication Fields of Elliptic Curves over Finite Fields

Florian Luca, Igor E. Shparlinski

• We show that, for most of the elliptic curves E over a prime finite field Fp of p elements, the discriminant D(E) of the quadratic number field containing the endomorphism ring of E over Fp 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 Fp.