Murmurations, Mestre--Nagao sums, and Convolutional Neural Networks for elliptic curves
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arXiv
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| Main Authors: | , , , , , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866917351607238656 |
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| author | Bieri, Joanna Costa, Edgar Deines, Alyson Lee, Kyu-Hwan Lowry-Duda, David Oliver, Thomas Qi, Yidi Veenstra, Tamara |
| author_facet | Bieri, Joanna Costa, Edgar Deines, Alyson Lee, Kyu-Hwan Lowry-Duda, David Oliver, Thomas Qi, Yidi Veenstra, Tamara |
| contents | 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, Bujanović--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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_17681 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Murmurations, Mestre--Nagao sums, and Convolutional Neural Networks for elliptic curves Bieri, Joanna Costa, Edgar Deines, Alyson Lee, Kyu-Hwan Lowry-Duda, David Oliver, Thomas Qi, Yidi Veenstra, Tamara Number Theory Machine Learning 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, Bujanović--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. |
| title | Murmurations, Mestre--Nagao sums, and Convolutional Neural Networks for elliptic curves |
| topic | Number Theory Machine Learning |
| url | https://arxiv.org/abs/2603.17681 |