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Elliptic Curves of Large Rank and Small Conductor

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Algorithmic Number Theory (ANTS 2004)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 3076))

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Abstract

For r=6,7,...,11 we find an elliptic curve E/Q of rank at least r and the smallest conductor known, improving on the previous records by factors ranging from 1.0136 (for r=6) to over 100 (for r=10 and r=11). We describe our search methods, and tabulate, for each r=5,6,...,11, the five curves of lowest conductor, and (except for r=11) also the five of lowest absolute discriminant, that we found.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Harvard University, Cambridge, MA, 02138, USA

    Noam D. Elkies

  2. The Pennsylvania State University,  

    Mark Watkins

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  1. Noam D. Elkies
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  2. Mark Watkins
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Editors and Affiliations

  1. Department of Computer Science and Engineering, University of South Carolina , SC 29208, Columbia, USA

    Duncan Buell

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Elkies, N.D., Watkins, M. (2004). Elliptic Curves of Large Rank and Small Conductor. In: Buell, D. (eds) Algorithmic Number Theory. ANTS 2004. Lecture Notes in Computer Science, vol 3076. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24847-7_3

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  • DOI: https://doi.org/10.1007/978-3-540-24847-7_3

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-22156-2

  • Online ISBN: 978-3-540-24847-7

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