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Ranks of elliptic curves in cubic extensions

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Number Theory, Analysis and Geometry

Abstract

Let E ∕ ℚbe an elliptic curve defined over the rational field ℚ. We examine the rank of the Mordell–Weil group E(K) as Kranges over cubic extensions ofℚ.

Mathematics Subject Classification (2010): 11G05, 11R16, 14H52

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Acknowledgments

This work was supported in part by a grant from NSERC.

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Authors and Affiliations

  1. Department of Mathematics and Statistics and CICMA, Concordia University, 1455 de Maisonneuve Blvd. West, Montréal, Quebec, H3G 1M8, Canada

    Hershy Kisilevsky

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  1. Hershy Kisilevsky
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Correspondence to Hershy Kisilevsky .

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Editors and Affiliations

  1. , Department of Mathematics, Columbia University, Broadway 2990, New York, 10027, New York, USA

    Dorian Goldfeld

  2. , Department of Mathematics, City College of New York, New York, 10031, New York, USA

    Jay Jorgenson

  3. , Department of Mathematics, Yale University, Hillhouse Ave. 10, New Haven, 06520, Connecticut, USA

    Peter Jones

  4. , Department of Mathematics, California Institute of Technology, E. California Blvd. 1200, Pasadena, 91125, California, USA

    Dinakar Ramakrishnan

  5. , Department of Mathematics, University of California at Berkeley, Evans Hall 925, Berkeley, 94720-3840, California, USA

    Kenneth Ribet

  6. , Department of Mathematics, Harvard University, Science Center/One Oxford Street, Cambridge, 02138, Massachusetts, USA

    John Tate

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Dedicated to the memory of S. Lang

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Kisilevsky, H. (2012). Ranks of elliptic curves in cubic extensions. In: Goldfeld, D., Jorgenson, J., Jones, P., Ramakrishnan, D., Ribet, K., Tate, J. (eds) Number Theory, Analysis and Geometry. Springer, Boston, MA. https://doi.org/10.1007/978-1-4614-1260-1_17

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