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 SwinnertonDyer conjectures for modular jacobians of genus 2 curves. Mathematics of Computation, 70 . pp. 16751697. ISSN 00255718

PDF
296kB 
Abstract
This paper provides empirical evidence for the Birch and SwinnertonDyer 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 ShafarevichTate 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 2torsion of the ShafarevichTate group, which we could compute.
Item Type:  Article 

Uncontrolled Keywords:  Birch and SwinnertonDyer 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:  29 May 2015 18:19 
Repository Staff Only: item control page