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

Title data

Flynn, E. Victor ; Leprévost, Franck ; Schaefer, Edward F. ; Stein, William A. ; Stoll, Michael ; Wetherell, Joseph L.:
Empirical evidence for the Birch and Swinnerton-Dyer conjectures for modular Jacobians of genus 2 curves.
In: Mathematics of Computation. Vol. 70 (2001) Issue 236 . - pp. 1675-1697.
ISSN 0025-5718
DOI: https://doi.org/10.1090/S0025-5718-01-01320-5

Abstract in another language

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.

Further data

Item Type: Article in a journal
Refereed: Yes
Keywords: Birch and Swinnerton-Dyer conjecture; genus 2; Jacobian; modular abelian variety
Institutions of the University: Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics II
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics II > Chair Mathematics II - Univ.-Prof. Dr. Michael Stoll
Faculties
Faculties > Faculty of Mathematics, Physics und Computer Science
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics
Result of work at the UBT: No
DDC Subjects: 500 Science > 510 Mathematics
Date Deposited: 03 Feb 2015 10:32
Last Modified: 03 Feb 2015 10:32
URI: https://eref.uni-bayreuth.de/id/eprint/6231