Some minimisation algorithms in arithmetic invariant theory
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Authors
Fisher, TA
Radicevic, Lazar
Publication Date
2018Journal Title
Journal de Theorie des Nombres de Bordeaux
ISSN
1246-7405
Publisher
Universite de Bordeaux III
Volume
30
Issue
3
Pages
801-828
Type
Article
Metadata
Show full item recordCitation
Fisher, T., & Radicevic, L. (2018). Some minimisation algorithms in arithmetic invariant theory. Journal de Theorie des Nombres de Bordeaux, 30 (3), 801-828. https://doi.org/10.5802/jtnb.1050
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.
Keywords
elliptic curves, genus one curves, minimisation, coregular representations
Identifiers
External DOI: https://doi.org/10.5802/jtnb.1050
This record's URL: https://www.repository.cam.ac.uk/handle/1810/280029
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