Some minimisation algorithms in arithmetic invariant theory
Accepted version
Peer-reviewed
Repository URI
Repository DOI
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
2118-8572
Volume Title
30
Publisher
Universite de Bordeaux III