Discriminants of Complex Multiplication Fields of Elliptic Curves over Finite Fields

• Autores: Florian Luca, Igor E. Shparlinski
• Localización: Canadian mathematical bulletin, ISSN 0008-4395, Vol. 50, Nº 3, 2007, págs. 409-417
• Idioma: inglés
• DOI: 10.4153/cmb-2007-039-2
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• Resumen

  • 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.