Murmurations, Mestre–Nagao sums, and Convolutional Neural Networks for elliptic curves

This repository contains the official codebase for the paper "Murmurations, Mestre–Nagao sums, and Convolutional Neural Networks for elliptic curves".

Overview

This project applies machine learning techniques to number theory by exploring the predictions of Convolutional Neural Networks (CNNs) on the rank of elliptic curves. We provide tools to interpret these predictions using saliency curves and investigate the interesting interplay between murmurations and Mestre–Nagao sums. The codebase includes scripts for generating datasets, training the CNN models, and reproducing the saliency curve analysis detailed in the paper.

Citation

If you use this codebase or find our work helpful in your research, please cite our paper using the following BibTeX entry:

@misc{bieri2026murmurationsmestrenagaosumsconvolutional,
      title={Murmurations, Mestre--Nagao sums, and Convolutional Neural Networks for elliptic curves}, 
      author={Joanna Bieri and Edgar Costa and Alyson Deines and Kyu-Hwan Lee and David Lowry-Duda and Thomas Oliver and Yidi Qi and Tamara Veenstra},
      year={2026},
      eprint={2603.17681},
      archivePrefix={arXiv},
      primaryClass={math.NT},
      url={https://arxiv.org/abs/2603.17681}, 
}