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Some minimisation algorithms in arithmetic invariant theory

Accepted version
Peer-reviewed

Type

Article

Change log

Authors

Fisher, TA 
Radicevic, Lazar 

Abstract

We extend the work of Cremona, Fisher and Stoll on minimising genus one curves of degrees 2,3,4,5, to some of the other representations associated to genus one curves, as studied by Bhargava and Ho. Specifically we describe algorithms for minimising bidegree (2,2)-forms, 3 x 3 x 3 cubes and 2 x 2 x 2 x 2 hypercubes. We also prove a theorem relating the minimal discriminant to that of the Jacobian elliptic curve.

Description

Keywords

elliptic curves, genus one curves, minimisation, coregular representations

Journal Title

Journal de Theorie des Nombres de Bordeaux

Conference Name

Journal ISSN

1246-7405
2118-8572

Volume Title

30

Publisher

Universite de Bordeaux III