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2010 Minimisation and reduction of 2-, 3- and 4-coverings of elliptic curves
John E. Cremona, Tom A. Fisher, Michael Stoll
Algebra Number Theory 4(6): 763-820 (2010). DOI: 10.2140/ant.2010.4.763

Abstract

We consider models for genus-one curves of degree n for n=2, 3 and 4, which arise in explicit n-descent on elliptic curves. We prove theorems on the existence of minimal models with the same invariants as the minimal model of the Jacobian elliptic curve and provide simple algorithms for minimising a given model, valid over general number fields. Finally, for genus-one models defined over , we develop a theory of reduction and again give explicit algorithms for n=2, 3 and 4.

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John E. Cremona. Tom A. Fisher. Michael Stoll. "Minimisation and reduction of 2-, 3- and 4-coverings of elliptic curves." Algebra Number Theory 4 (6) 763 - 820, 2010. https://doi.org/10.2140/ant.2010.4.763

Information

Received: 19 January 2010; Accepted: 18 July 2010; Published: 2010
First available in Project Euclid: 20 December 2017

zbMATH: 1222.11073
MathSciNet: MR2728489
Digital Object Identifier: 10.2140/ant.2010.4.763

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

Rights: Copyright © 2010 Mathematical Sciences Publishers

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Vol.4 • No. 6 • 2010
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