Skip to Main Content

Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Explicit $n$-descent on elliptic curves III. Algorithms
HTML articles powered by AMS MathViewer

by J. E. Cremona, T. A. Fisher, C. O’Neil, D. Simon and M. Stoll PDF
Math. Comp. 84 (2015), 895-922 Request permission


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 $\mathbb {P}^{n-1}$. 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.

Similar Articles
  • Retrieve articles in Mathematics of Computation with MSC (2010): 11G05, 14H25, 14H52
  • Retrieve articles in all journals with MSC (2010): 11G05, 14H25, 14H52
Additional Information
  • J. E. Cremona
  • Affiliation: Mathematics Institute, University of Warwick, Coventry CV4 7AL, United Kingdom
  • MR Author ID: 52705
  • ORCID: 0000-0002-7212-0162
  • Email:
  • T. A. Fisher
  • Affiliation: University of Cambridge, DPMMS, Centre for Mathematical Sciences, Wilberforce Road, Cambridge CB3 0WB, United Kingdom
  • MR Author ID: 678544
  • Email:
  • C. O’Neil
  • Affiliation: 505 Pulitzer Hall, Columbia University Graduate School of Journalism, 2950 Broadway, New York, New York 10027
  • Email:
  • D. Simon
  • Affiliation: Université de Caen, Campus II - Boulevard Maréchal Juin, BP 5186–14032, Caen, France
  • Email:
  • M. Stoll
  • Affiliation: Mathematisches Institut, Universität Bayreuth, 95440 Bayreuth, Germany
  • Email:
  • Received by editor(s): August 31, 2012
  • Received by editor(s) in revised form: June 4, 2013, and June 28, 2013
  • Published electronically: July 29, 2014
  • © Copyright 2014 American Mathematical Society
  • Journal: Math. Comp. 84 (2015), 895-922
  • MSC (2010): Primary 11G05, 14H25, 14H52
  • DOI:
  • MathSciNet review: 3290968