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Archimedean local height differences on elliptic curves

Volume 190 / 2019

J. Steffen Müller, Corinna Stumpe Acta Arithmetica 190 (2019), 293-303 MSC: Primary 11G50; Secondary 14G05, 11G05, 11G07. DOI: 10.4064/aa180714-7-12 Published online: 5 July 2019


To compute generators for the Mordell–Weil group of an elliptic curve over a number field, one needs to bound from above the difference between the naive and the canonical height. We give an elementary and fast method to compute an upper bound for the local contribution to this difference at an archimedean place, which typically gives better results than previously known algorithms.


  • J. Steffen MüllerBernoulli Institute
    University of Groningen
    Nijenborgh 9
    9747 AG Groningen, The Netherlands
  • Corinna StumpeInstitut für Mathematik
    Carl von Ossietzky Universität Oldenburg
    26111 Oldenburg, Germany

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