Datasets:
Modalities:
Image
Formats:
imagefolder
Languages:
English
Size:
< 1K
Tags:
mathematics
number-theory
elliptic-curves
bsd-conjecture
scientific-computing
algebraic-geometry
License:
Update README.md
Browse files
README.md
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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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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.
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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.
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curve_id:
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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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task_categories:
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- image-classification
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- image-to-text
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- tabular-classification
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tags:
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- mathematics
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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.
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This Dataset is a collection of computational data relating to elliptic curves and their associated L-functions. The 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.
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## Dataset Summary
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The Birch and Swinnerton-Dyer conjecture is a Millennium Prize Problem that connects the algebraic rank of an elliptic curve to
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the behavior of its L-function at a critical point.
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This dataset provides the necessary numerical features (coefficients, conductors, and L-values) to explore these relationships
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empirically.
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## Supported Tasks Rank Regression:
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Predict the algebraic rank of an elliptic curve as a continuous or integer value based on analytic data.
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## Analytic Rank Classification:
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Classify curves into rank categories (e.g., Rank 0 vs. Rank 1).
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## Feature Exploration:
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Study the correlation between coefficients \(a_{1},a_{2},\dots \) and the curve's global invariants.
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## Dataset Structure
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The data is typically provided in a tabular format (CSV or Parquet).
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## Common columns include:
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curve_id:
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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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