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Minimisation and reduction of 2-, 3- and 4-coverings of elliptic curves
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Cremona, J. E., Fisher, Tom A. and Stoll, Michael (2010) Minimisation and reduction of 2-, 3- and 4-coverings of elliptic curves. Algebra & Number Theory, Vol.4 (No.6). pp. 763-820. doi:10.2140/ant.2010.4.763 ISSN 1937-0652.
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Official URL: http://dx.doi.org/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 Q, we develop a theory of reduction and again give explicit algorithms for n = 2, 3 and 4.
| Item Type: | Journal Article | ||||
|---|---|---|---|---|---|
| Subjects: | Q Science > QA Mathematics | ||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
| Journal or Publication Title: | Algebra & Number Theory | ||||
| Publisher: | Mathematical Sciences Publishers | ||||
| ISSN: | 1937-0652 | ||||
| Official Date: | 2010 | ||||
| Dates: |
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| Volume: | Vol.4 | ||||
| Number: | No.6 | ||||
| Number of Pages: | 58 | ||||
| Page Range: | pp. 763-820 | ||||
| DOI: | 10.2140/ant.2010.4.763 | ||||
| Status: | Peer Reviewed | ||||
| Publication Status: | Published | ||||
| Access rights to Published version: | Restricted or Subscription Access |
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