Titlebar

Export bibliographic data
Literature by the same author
plus on the publication server
plus at Google Scholar

 

Minimisation and reduction of 2-, 3- and 4-coverings of elliptic curves

Title data

Cremona, John E. ; Fisher, Tom A. ; Stoll, Michael:
Minimisation and reduction of 2-, 3- and 4-coverings of elliptic curves.
In: Algebra & Number Theory. Vol. 4 (25 September 2010) Issue 6 . - pp. 763-820.
ISSN 1937-0652
DOI: https://doi.org/10.2140/ant.2010.4.763

Abstract in another language

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 Q, we develop a theory of reduction and again give explicit algorithms for n = 2, 3 and 4.

Further data

Item Type: Article in a journal
Refereed: Yes
Keywords: elliptic curves; genus-one curves; minimisation; reduction; descent
Institutions of the University: Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics II
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics II > Chair Mathematics II - Univ.-Prof. Dr. Michael Stoll
Faculties
Faculties > Faculty of Mathematics, Physics und Computer Science
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics
Result of work at the UBT: Yes
DDC Subjects: 500 Science > 510 Mathematics
Date Deposited: 21 Jan 2015 13:38
Last Modified: 10 Feb 2015 12:01
URI: https://eref.uni-bayreuth.de/id/eprint/5761