Empirical evidence for the Birch and Swinnerton-Dyer conjectures for modular Jacobians of genus 2 curves-Reference-Cited by-同舟云学术

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

Published:2001-05-11 Issue:236 Volume:70 Page:1675-1697
ISSN:0025-5718
Container-title:Mathematics of Computation
language:en
Short-container-title:Math. Comp.

Author:

Flynn E.,Leprévost Franck,Schaefer Edward,Stein William,Stoll Michael,Wetherell Joseph

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.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,Computational Mathematics,Algebra and Number Theory

Link

http://www.ams.org/mcom/2001-70-236/S0025-5718-01-01320-5/S0025-5718-01-01320-5.pdf

Reference46 articles.

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