Work

A Twelve-Curve Computation Toward Resolution of the Birch and Swinnerton-Dyer Conjecture

Year: 2025

Type: article

Abstract: This work presents a numerical investigation of the Birch and Swinnerton-Dyer (BSD) conjecture using SageMath. Twelve elliptic curves over the rational field are analyzed, spanning ranks from 0 to 3 and representing diverse torsion structures and conductors. For each curve, we compute rank, torsion subgroup, L-function value (via the Dokchitser method), regulator, conductor, discriminant, and Tamagawa numbers. The numerical results consistently support the BSD identity across all tested cases.

Source: Zenodo (CERN European Organization for Nuclear Research)

DOI: 10.5281/zenodo.15203063

Authors: McCormick, Andre L, Seneca, Sol

Language: English

Topic: Analytic Number Theory Research

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W6930514130

FWCI:

Cites:

Cited by:

Related to: