Discriminants of complex multiplication fields of elliptic curves over finite fields

Florian Luca*, Igor E. Shparlinski

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)

Abstract

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

Original languageEnglish
Pages (from-to)409-417
Number of pages9
JournalCanadian Mathematical Bulletin
Volume50
Issue number3
Publication statusPublished - Sep 2007

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