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Explicit n-descent on elliptic curves. III. Algorithms
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Cremona, J. E., Fisher, Tom, O'Neil, Cathy, Simon, Denis and Stoll, Michael (2011) Explicit n-descent on elliptic curves. III. Algorithms. Working Paper. ArXiv e-prints. ArXiv e-prints (No.1107.3516v1).
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Official URL: http://arxiv.org/pdf/1107.3516v1.pdf
Abstract
This is the third in a series of papers in which we study the n-Selmer group of an elliptic curve, with the aim of representing its elements as genus one normal curves of degree n. The methods we describe are practical in the case n = 3 for elliptic curves over the rationals, and have been implemented in MAGMA.
One important ingredient of our work is an algorithm for trivialising central simple algebras. This is of independent interest: for example, it could be used for parametrising Brauer-Severi surfaces.
| Item Type: | Working or Discussion Paper (Working Paper) | ||||
|---|---|---|---|---|---|
| Subjects: | Q Science > QA Mathematics | ||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
| Series Name: | ArXiv e-prints | ||||
| Publisher: | ArXiv e-prints | ||||
| Official Date: | 18 June 2011 | ||||
| Dates: |
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| Number: | No.1107.3516v1 | ||||
| Number of Pages: | 42 | ||||
| Institution: | University of Warwick | ||||
| Status: | Not Peer Reviewed | ||||
| Publication Status: | Published | ||||
| Access rights to Published version: | Open Access (Creative Commons) | ||||
| Related URLs: |
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