Work

Numerical Exploration of the BSD Conjecture Through 12 Verified Elliptic Curves

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. Key invariants are computed and the BSD identity is numerically verified in each case. The paper also introduces symbolic implications relating to modular resonance, phantom points, and higher-dimensional harmonic structure.

Source: Zenodo (CERN European Organization for Nuclear Research)

DOI: 10.5281/zenodo.15204740

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: W6930612925

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