Numerical Exploration of the BSD Conjecture Through 12 Verified Elliptic Curves

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.

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2025-04-13
DOI
https://doi.org/10.5281/zenodo.15204740
Primary Topic
Cryptography and Residue Arithmetic
Type
article
Field-Weighted Citation Impact
0.00
Controls
|||
ALL TIME
JAN
FEB
MAR
APR
MAY
JUN
JUL
AUG
SEP
OCT
article

Numerical Exploration of the BSD Conjecture Through 12 Verified Elliptic Curves

Zenodo (CERN European Organization for Nuclear Research)
Cryptography and Residue Arithmetic
article

Numerical Exploration of the BSD Conjecture Through 12 Verified Elliptic Curves

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. 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.

Zenodo (CERN European Organization for Nuclear Research)
Openalex Percentile: Top 41%
Cryptography and Residue Arithmetic
DOIOpen Access PDFOpenAlex
AI Navigator

Ask Laika to Summarize, Analyze, and Connect papers live on the map.

Summarize Papers & Methodologies

Extract key findings, datasets, and comparative methods across publications.

Benchmark Rankings & Visual Analytics

Rank top research institutions, authors, funders, topics, and journals by Field-Weighted Citation Impact (FWCI) and paper volume with instant charts.

Connect Distant Disciplines

Bridge topological clusters on the map to find hidden collaborative intersections.

Numerical Exploration of the BSD Conjecture Through 12 Verified Elliptic Curves · Zenodo (CERN European Organization for Nuclear Research) (2025) | TGRS Research Map | TGRS