Vol. 7, No. 5, 2013

Download this article
Download this article For screen
For printing
Recent Issues

Volume 10
Issue 9, 1845–2052
Issue 8, 1601–1843
Issue 7, 1373–1600
Issue 6, 1147–1371
Issue 5, 939–1146
Issue 4, 695–938
Issue 3, 451–694
Issue 2, 215–450
Issue 1, 1–214

Volume 9, 10 issues

Volume 8, 10 issues

Volume 7, 10 issues

Volume 6, 8 issues

Volume 5, 8 issues

Volume 4, 8 issues

Volume 3, 8 issues

Volume 2, 8 issues

Volume 1, 4 issues

The Journal
Cover
Editorial Board
Editors' Addresses
Editors' Interests
About the Journal
Scientific Advantages
Submission Guidelines
Submission Form
Subscriptions
Editorial Login
Contacts
Author Index
To Appear
 
ISSN: 1944-7833 (e-only)
ISSN: 1937-0652 (print)
Minimisation and reduction of 5-coverings of elliptic curves

Tom Fisher

Vol. 7 (2013), No. 5, 1179–1205
Abstract

We consider models for genus-1 curves of degree 5, which arise in explicit 5-descent on elliptic curves. We prove a theorem on the existence of minimal models with the same invariants as the minimal model of the Jacobian elliptic curve and give an algorithm for computing such models. Finally we describe how to reduce genus-1 models of degree 5 defined over .

Keywords
elliptic curves, genus-$1$ curves, minimisation, reduction, descent
Mathematical Subject Classification 2010
Primary: 11G05
Secondary: 11G07, 14H52, 14H25
Milestones
Received: 2 February 2012
Accepted: 20 August 2012
Published: 6 September 2013
Authors
Tom Fisher
Department of Pure Mathematics and Mathematical Statistics
University of Cambridge
Wilberforce Road
Cambridge
CB3 0WB
United Kingdom
http://www.dpmms.cam.ac.uk/~taf1000/