CMS/SMC
Canadian Mathematical Society
www.cms.math.ca
Canadian Mathematical Society
  location:  PublicationsjournalsCMB
Publications        
Abstract view

Discriminants of Complex Multiplication Fields of Elliptic Curves over Finite Fields

  Published:2007-09-01
 Printed: Sep 2007
  • Florian Luca
  • Igor E. Shparlinski
Format:   HTML   LaTeX   MathJax   PDF   PostScript  

Abstract

We show that, for most of the elliptic curves $\E$ over a prime finite field $\F_p$ of $p$ elements, the discriminant $D(\E)$ of the quadratic number field containing the endomorphism ring of $\E$ over $\F_p$ 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 $\F_p$.
MSC Classifications: 11G20, 11N32, 11R11 show english descriptions Curves over finite and local fields [See also 14H25]
Primes represented by polynomials; other multiplicative structure of polynomial values
Quadratic extensions
11G20 - Curves over finite and local fields [See also 14H25]
11N32 - Primes represented by polynomials; other multiplicative structure of polynomial values
11R11 - Quadratic extensions
 

© Canadian Mathematical Society, 2014 : https://cms.math.ca/