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Explicit n-descent on elliptic curves III. Algorithms

Title data

Cremona, John E. ; Fisher, Tom A. ; O'Neil, C. ; Simon, D. ; Stoll, Michael:
Explicit n-descent on elliptic curves III. Algorithms.
In: Mathematics of Computation. Vol. 84 (March 2015) Issue 292 . - pp. 895-922.
ISSN 0025-5718
DOI: https://doi.org/10.1090/S0025-5718-2014-02858-5

Abstract in another language

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 curves of degree n in P^(n-1). 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.

Further data

Item Type: Article in a journal
Refereed: Yes
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 13:31
Last Modified: 14 Apr 2015 07:31
URI: https://eref.uni-bayreuth.de/id/eprint/5757