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Machine Learning Approaches to the Shafarevich-Tate Group of Elliptic Curves

This is the codebase for the paper of the same name, by Angelica Babei, Barinder S. Banwait, AJ Fong, Xiaoyu Huang, and Deependra Singh.

How do I reproduce the results in your paper?

You will first need the datafiles. These must be placed in a subdirectory called "sha" in the data_files folder. The data we have used for this project has been obtained from the LMFDB. For the reader's convenience, it may be downloaded from here and here (both are used in the notebooks, but this latter one is the more relevant one). We cannot have this in the github repo because it is far too large. The reader is encouraged to download these files and place them in the sha subdirectory of data_files.

Once you've got the data files there, you will find all relevant code in the various .ipynb files in the experiments folder.

Directory structure

.
├── ml_rnt              # Main project directory
│   ├── data_files      # Where the data is stored
│   ├── python          # Python scripts for data processing and modeling
│   ├── experiments     # Jupyter notebooks for experiments and analyses
│   ├── trained_models  # Used for storing large NN models that take time to train
│   ├── LICENSE         # License for the project
│   ├── README.md       # Project description and setup instructions
│   ├── .gitignore      # Git ignore file for unwanted files

Copyright

####  Copyright (C) 2024 The Authors: Angelica Babei, Barinder S. Banwait,
AJ Fong, Xiaoyu Huang, and Deependra Singh.

The code found throughout this repository  is free software: you can
redistribute it and/or modify it under the terms of the GNU General
Public License as published by the Free Software Foundation, either
version 3 of the License, or any later version.

This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
GNU General Public License for more details.

You should have received a copy of the GNU General Public License
along with this program.  If not, see <https://www.gnu.org/licenses/>.

The authors can be reached at the email addresses stated in the paper
linked to above.

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