Champion primes for elliptic curves
type: Item
instance of: scholarly article
zbMATH Open document ID: 1342.11058
author: Hui Xue
author: Jason Hedetniemi
author: Kevin James
publication date: 2014-10-23T00:00:00Z
full work available at URL: o53.Abstract.html
Mathematics Subject Classification ID: 11G05
zbMATH DE Number: 6360725
zbMATH Keywords: elliptic curve
zbMATH Keywords: champion prime
MaRDI profile type: Publication
title: Champion primes for elliptic curves
published in: Integers
review text: Let \(E_{a,b}\) be the elliptic curve \(y^2=x^3+ax+b\) over the finite field \(\mathbb F_p\) with \(p\) prime. If \(E_{a,b}\) is nonsingular over \(\mathbb F_p\) and \(\#E_{a,b}(\mathbb F_p)=p+1+\lfloor 2\sqrt p\rfloor\), then \(p\) is called a champion prime for \(E_{a,b}\). In the paper under review, the authors study champion primes for elliptic curves. One of their results is that the set of elliptic curves with trace of Frobenius at p a minimum has density one.
reviewed by: Zhi-Wei Sun
description: scientific article; zbMATH DE number 6360725