A family of elliptic curves of large rank
type: Item
instance of: scholarly article
title: A family of elliptic curves of large rank
zbMATH Open document ID: 1264.11047
author: Thomas Occhipinti
published in: Journal of Number Theory
publication date: 2012-03-19T00:00:00Z
review text: Let \(k\) be a finite field and \(d\) a positive integer not divisible by the characteristic of \(k\). For each \(a \in k\) let \(E\) be the elliptic curve defined by the equation \(x(x-1)(y-a) = t^dy(y-1)(x-a)\) over \(k(t)\). In this article it is shown that the conjecture of Birch and Swinnerton-Dyer holds for \(E\), and that \(E\) has rank at least \(d\) over \(\mathbb F_q(t)\) if \(d\) divides \(q-1\), and that the rank over \(\overline{\mathbb F_q}(t)\) is at least \(d\) if \(d\) is coprime to \(q\).
reviewed by: Franz Lemmermeyer
Mathematics Subject Classification ID: 11G05
Mathematics Subject Classification ID: 11G40
zbMATH DE Number: 6015646
zbMATH Keywords: elliptic curves
zbMATH Keywords: function field
zbMATH Keywords: conjecture of Birch and Swinnerton-Dyer
zbMATH Keywords: zeta function
zbMATH Keywords: L-function
zbMATH Keywords: Mordell-Weil rank
MaRDI profile type: Publication
full work available at URL: j.jnt.2011.10.003
OpenAlex ID: W2040853309
cites work: Q4434669
cites work: Towers of surfaces dominated by products of curves and elliptic curves of large rank over function fields
cites work: Q3871006
cites work: Elliptic Surfaces
cites work: Q5555474
cites work: Q4317891
cites work: \(L\)-functions with large analytic rank and abelian varieties with large algebraic rank over function fields
DOI: 10.1016/J.JNT.2011.10.003
description: scientific article; zbMATH DE number 6015646