Vol. 7, No. 5, 2013

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Minimisation and reduction of 5-coverings of elliptic curves

Tom Fisher

Vol. 7 (2013), No. 5, 1179–1205

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 .

elliptic curves, genus-$1$ curves, minimisation, reduction, descent
Mathematical Subject Classification 2010
Primary: 11G05
Secondary: 11G07, 14H52, 14H25
Received: 2 February 2012
Accepted: 20 August 2012
Published: 6 September 2013
Tom Fisher
Department of Pure Mathematics and Mathematical Statistics
University of Cambridge
Wilberforce Road
United Kingdom