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arXiv · 2603.17681

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

Joanna Bieri·Edgar Costa·Alyson Deines·Kyu-Hwan Lee·David Lowry-Duda·Thomas Oliver·Yidi Qi·Tamara Veenstra
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Abstract

We apply one-dimensional convolutional neural networks to the Frobenius traces of elliptic curves over $\mathbb{Q}$ 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 murmurations and Mestre--Nagao sums, the details of which vary with the conductor and the (predicted) rank.

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Joanna Bieri, Edgar Costa, Alyson Deines, Kyu-Hwan Lee, David Lowry-Duda, Thomas Oliver, Yidi Qi, Tamara Veenstra. 2026-03-18. Murmurations, Mestre--Nagao sums, and Convolutional Neural Networks for elliptic curves. https://arxiv.org/abs/2603.17681

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