Vol. 1, No. 1, 2013

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Conditionally bounding analytic ranks of elliptic curves

Jonathan W. Bober

Vol. 1 (2013), No. 1, 135–144

We describe a method for bounding the rank of an elliptic curve under the assumptions of the Birch and Swinnerton-Dyer conjecture and the generalized Riemann hypothesis. As an example, we compute, under these conjectures, exact upper bounds for curves which are known to have rank at least as large as 20,21,22,23, and 24. For the known curve of rank at least 28, we get a bound of 30.

elliptic curve, rank, L-function, explicit formula
Mathematical Subject Classification 2010
Primary: 11M41
Secondary: 14G10
Published: 14 November 2013
Jonathan W. Bober
Department of Mathematics
University of Washington
Seattle, WA 98195-4350
United States
Howard House
University of Bristol
Queens Avenue
Bristol BS8 1SN United Kingdom