2025/09/23 by UTHIT LAKKAEW
Mathematics · #Analysis #Birch and Swinnerton-Dyer Conjecture #Computer Sciences #Elliptic Curves #FOS: Mathematics #High-Precision Computation #L-Functions #Mathematical Visualization #Mathematics #Nonlinear #Number Theory #Numerical Analysis and Scientific Computing #Physical Sciences and Mathematics #Physics #Reproducible Research #SageMath #SageMath 10.7 #Statistical #and Soft Matter Physics
paper · doi:10.17605/osf.io/jegup
This project provides a high-precision numeric evaluation of the Birch and Swinnerton-Dyer (BSD) Conjecture for selected elliptic curves over ℚ. We compute canonical heights, regulators, torsion subgroup orders, Tamagawa products, L-series derivatives, and BSD predictions with 50-digit precision using SageMath 10.7. The evaluation includes curves of rank 0, 1, and 3, highlighting the computation of canonical height matrices for rank >1 curves. Visualization of results via log-scale bar plots is provided. This dataset complements existing data from LMFDB and allows verification of analytic ranks and BSD-related quantities. The project includes full reproducible SageMath code for numeric evaluation and plotting, making it suitable for researchers and students interested in explicit BSD computations. All numeric results are cross-checked for accuracy, including correction of previous inconsistencies in regulator values and BSD predictions.