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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.


Computing canonical heights using arithmetic intersection theory
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by Jan Steffen Müller PDF
Math. Comp. 83 (2014), 311-336 Request permission


For several applications in the arithmetic of abelian varieties it is important to compute canonical heights. Following Faltings and Hriljac, we show how the canonical height of a point on the Jacobian of a smooth projective curve can be computed using arithmetic intersection theory on a regular model of the curve in practice. In the case of hyperelliptic curves we present a complete algorithm that has been implemented in Magma. Several examples are computed and the behavior of the running time is discussed.
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Additional Information
  • Jan Steffen Müller
  • Affiliation: Fachbereich Mathematik, Universität Hamburg
  • MR Author ID: 895560
  • Email:
  • Received by editor(s): June 29, 2011
  • Received by editor(s) in revised form: January 27, 2012, and March 5, 2012
  • Published electronically: June 14, 2013
  • Additional Notes: This work was supported by DFG-grant STO 299/5-1
  • © Copyright 2013 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Math. Comp. 83 (2014), 311-336
  • MSC (2010): Primary 11G50; Secondary 11G10, 11G30, 14G40
  • DOI:
  • MathSciNet review: 3120591