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

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.

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2025-04-12
DOI
https://doi.org/10.5281/zenodo.15203064
Primary Topic
Literature, Language, and Rhetoric Studies
Type
article
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article

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

Zenodo (CERN European Organization for Nuclear Research)
Literature, Language, and Rhetoric Studies
article

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

article en

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.

Zenodo (CERN European Organization for Nuclear Research)
Reduced inequalities
Openalex Percentile: Top 45%
Literature, Language, and Rhetoric Studies
DOIOpen Access PDFOpenAlex
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A Twelve-Curve Computation Toward Resolution of the Birch and Swinnerton-Dyer Conjecture · Zenodo (CERN European Organization for Nuclear Research) (2025) | TGRS Research Map | TGRS