The Mathematical Institute, University of Oxford, Eprints Archive

Empirical evidence for the Birch and Swinnerton-Dyer conjectures for modular jacobians of genus 2 curves

Flynn, E. V. and Leprévost, F. and Schaefer, E. F. and Stein, W. A. and Stoll, M. and Wetherell, J. L. (2001) Empirical evidence for the Birch and Swinnerton-Dyer conjectures for modular jacobians of genus 2 curves. Mathematics of Computation, 70 . pp. 1675-1697. ISSN 0025-5718

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Abstract

This paper provides empirical evidence for the Birch and Swinnerton-Dyer conjectures for modular Jacobians of genus 2 curves. The second of these conjectures relates six quantities associated to a Jacobian over the rational numbers. One of these six quantities is the size of the Shafarevich-Tate group. Unable to compute that, we computed the five other quantities and solved for the last one. In all 32 cases, the result is very close to an integer that is a power of 2. In addition, this power of 2 agrees with the size of the 2-torsion of the Shafarevich-Tate group, which we could compute.

Item Type:Article
Uncontrolled Keywords:Birch and Swinnerton-Dyer conjectures, Jacobian, modular abelian variety.
Subjects:A - C > Algebraic geometry
H - N > Number theory
Research Groups:Number Theory Group
ID Code:259
Deposited By:E. Victor Flynn
Deposited On:12 Jul 2006
Last Modified:20 Jul 2009 14:19

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