Datasets:
Modalities:
Image
Formats:
imagefolder
Languages:
English
Size:
< 1K
Tags:
mathematics
number-theory
elliptic-curves
bsd-conjecture
scientific-computing
algebraic-geometry
License:
Create README.md
Browse files
README.md
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---
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language:
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- en
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license: apache-2.0
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task_categories:
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- image-classification
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- image-to-text
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- computer-vision
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- table-regression
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- tabular-classification
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tags:
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- mathematics
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- number-theory
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- elliptic-curves
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- bsd-conjecture
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- scientific-computing
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- algebraic-geometry
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- multimodal
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- time-lapse
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- geometry
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- number-theory
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- elliptic-curves
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size_categories:
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- 100K<n<1M
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---
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## BSD Conjecture Dataset
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The BSD conjecture dataset concerns the Birch and Swinnerton-Dyer (BSD) Conjecture, a Millennium Prize problem in number
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theory. It typically contains numerical data on elliptic curves, such as coefficients, ranks, and L-function values, relevant for
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computational verification or machine learning applications in arithmetic geometry. The Birch and Swinnerton-Dyer (BSD) Conjecture
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Dataset is a collection of computational data relating to elliptic curves and their associated L-functions. This dataset is designed
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to support machine learning research in arithmetic geometry, specifically for predicting properties like the rank of an elliptic
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curve from its analytic invariants.Dataset SummaryThe Birch and Swinnerton-Dyer conjecture is a Millennium Prize Problem that
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connects the algebraic rank of an elliptic curve to the behavior of its L-function at a critical point. This dataset provides the
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necessary numerical features (coefficients, conductors, and L-values) to explore these relationships empirically.Supported TasksRank
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Regression: Predict the algebraic rank of an elliptic curve as a continuous or integer value based on analytic data.Analytic Rank
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Classification: Classify curves into rank categories (e.g., Rank 0 vs. Rank 1).Feature Exploration: Study the correlation between
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coefficients \(a_{1},a_{2},\dots \) and the curve's global invariants.Dataset StructureThe data is typically provided in a tabular
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format (CSV or Parquet).
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Common columns include:
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curve_id:
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Unique identifier for the elliptic curve.
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coefficients:
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The \([a_{1},a_{2},a_{3},a_{4},a_{6}]\) coefficients defining the curve.
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conductor:
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The conductor \(N\) of the curve.rank:
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The algebraic rank (target variable).l_value: The value or derivative of the L-function at \(s=1\).
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If you use this dataset in your research, please cite the original repository:
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bibtex@misc{bsd_conjecture_dataset,
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author = {webxos},
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title = {Birch and Swinnerton-Dyer Conjecture Dataset},
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year = {2026},
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publisher = {webXOS},
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journal = {2026},
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howpublished = {\url{webxos.netlify.app}}
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}
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