Open Access
2013 Minimisation and reduction of 5-coverings of elliptic curves
Tom Fisher
Algebra Number Theory 7(5): 1179-1205 (2013). DOI: 10.2140/ant.2013.7.1179


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 .


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Tom Fisher. "Minimisation and reduction of 5-coverings of elliptic curves." Algebra Number Theory 7 (5) 1179 - 1205, 2013.


Received: 2 February 2012; Accepted: 20 August 2012; Published: 2013
First available in Project Euclid: 20 December 2017

zbMATH: 1300.11058
MathSciNet: MR3101076
Digital Object Identifier: 10.2140/ant.2013.7.1179

Primary: 11G05
Secondary: 11G07 , 14H25 , 14H52

Keywords: descent , Elliptic curves , genus-$1$ curves , minimisation , reduction

Rights: Copyright © 2013 Mathematical Sciences Publishers

Vol.7 • No. 5 • 2013
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