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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.


Two-cover descent on hyperelliptic curves
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by Nils Bruin and Michael Stoll PDF
Math. Comp. 78 (2009), 2347-2370 Request permission


We describe an algorithm that determines a set of unramified covers of a given hyperelliptic curve, with the property that any rational point will lift to one of the covers. In particular, if the algorithm returns an empty set, then the hyperelliptic curve has no rational points. This provides a relatively efficiently tested criterion for solvability of hyperelliptic curves. We also discuss applications of this algorithm to curves of genus $1$ and to curves with rational points.
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Additional Information
  • Nils Bruin
  • Affiliation: Department of Mathematics, Simon Fraser University, Burnaby, BC, Canada V5A 1S6
  • MR Author ID: 653028
  • Email:
  • Michael Stoll
  • Affiliation: Mathematisches Institut, Universität Bayreuth, 95440 Bayreuth, Germany
  • Email:
  • Received by editor(s): March 31, 2008
  • Received by editor(s) in revised form: October 21, 2008
  • Published electronically: March 11, 2009
  • Additional Notes: The research of the first author was supported by NSERC
  • © Copyright 2009 American Mathematical Society
  • Journal: Math. Comp. 78 (2009), 2347-2370
  • MSC (2000): Primary 11G30; Secondary 14H40
  • DOI:
  • MathSciNet review: 2521292