Small discriminants of complex multiplication fields of elliptic curves over finite fields

Igor E. Shparlinski*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

We obtain a conditional, under the Generalized Riemann Hypothesis, lower bound on the number of distinct elliptic curves E over a prime finite field Fp of p elements, such that the discriminant D(E) of the quadratic number field containing the endomorphism ring of E over Fp is small. For almost all primes we also obtain a similar unconditional bound. These lower bounds complement an upper bound of F. Luca and I.E. Shparlinski (2007).

Original languageEnglish
Pages (from-to)381-388
Number of pages8
JournalCzechoslovak Mathematical Journal
Volume65
Issue number2
DOIs
Publication statusPublished - 26 Jun 2015
Externally publishedYes

Keywords

  • complex multiplication field
  • elliptic curve
  • Frobenius discriminant

Fingerprint Dive into the research topics of 'Small discriminants of complex multiplication fields of elliptic curves over finite fields'. Together they form a unique fingerprint.

Cite this