webxos/bsd_conjecture_dataset

BSD Conjecture Dataset

The BSD conjecture dataset concerns the Birch and Swinnerton-Dyer (BSD) Conjecture, a Millennium Prize problem in number theory. It typically contains numerical data on elliptic curves, such as coefficients, ranks, and L-function values, relevant for computational verification or machine learning applications in arithmetic geometry.

This Dataset is a collection of computational data relating to elliptic curves and their associated L-functions. The dataset is designed to support machine learning research in arithmetic geometry, specifically for predicting properties like the rank of an elliptic curve from its analytic invariants.

Dataset Summary

This dataset provides the necessary numerical features (coefficients, conductors, and L-values) to explore these relationships empirically.

Supported Tasks Rank Regression:

Predict the algebraic rank of an elliptic curve as a continuous or integer value based on analytic data.

Analytic Rank Classification:

Classify curves into rank categories (e.g., Rank 0 vs. Rank 1).

Feature Exploration:

Study the correlation between coefficients (a_{1},a_{2},\dots ) and the curve's global invariants.

Dataset Structure

The data is typically provided in a tabular format (CSV or Parquet).

Common columns include:

curve_id:

Unique identifier for the elliptic curve.

coefficients:

The ([a_{1},a_{2},a_{3},a_{4},a_{6}]) coefficients defining the curve.

conductor:

The conductor (N) of the curve.rank:

The algebraic rank (target variable).l_value: The value or derivative of the L-function at (s=1).

If you use this dataset in your research, please cite the original repository:

bibtex@misc{bsd_conjecture_dataset, author = {webxos}, title = {Birch and Swinnerton-Dyer Conjecture Dataset}, year = {2026}, publisher = {webXOS}, journal = {2026}, howpublished = {\url{webxos.netlify.app}} }