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

arXiv: https://arxiv.org/abs/2603.17681 · HTML: https://mlsanity.com/paper/2603.17681/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 18 references that are in the map.
- First posted on arXiv 18 Mar 2026.

## Builds on (most cited first, 4 of 4)

- [Machine-Learning the Sato--Tate Conjecture](https://mlsanity.com/paper/2010.01213/) (2020)
- [Murmurations of elliptic curves](https://mlsanity.com/paper/2204.10140/) (2022)
- [Machine-Learning Arithmetic Curves](https://mlsanity.com/paper/2012.04084/) (2020)
- [Machines Learn Number Fields, But How? The Case of Galois Groups](https://mlsanity.com/paper/2508.06670/) (2025)

## Built on by (most cited first, 2 of 2)

- [Transformers Learn the Mestre-Nagao Heuristic](https://mlsanity.com/paper/2606.15036/) (2026)
- [Decision trees, Frobenius traces, and Weierstrass coefficients of elliptic curves](https://mlsanity.com/paper/2607.24251/) (2026)

## Abstract (arXiv)

We apply one-dimensional convolutional neural networks to the Frobenius traces of elliptic curves over mathbbQ and evaluate and interpret their predictive capacity. In keeping with similar experiments by Kazalicki--Vlah, Bujanovi'c--Kazalicki--Novak, and Pozdnyakov, we observe high accuracy predictions for the analytic rank across a range of conductors. We interpret the prediction using saliency curves and explore the interesting interplay between saliency, murmurations and Mestre--Nagao sums.