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arXiv · 2502.10357

Learning Euler Factors of Elliptic Curves

Angelica Babei·François Charton·Edgar Costa·Xiaoyu Huang·Kyu-Hwan Lee·David Lowry-Duda·Ashvni Narayanan·Alexey Pozdnyakov
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Abstract

We apply transformer models and feedforward neural networks to predict Frobenius traces $a_p$ from elliptic curves given other traces $a_q$. We train further models to predict $a_p \bmod 2$ from $a_q \bmod 2$, and cross-analysis such as $a_p \bmod 2$ from $a_q$. Our experiments reveal that these models achieve high accuracy, even in the absence of explicit number-theoretic tools like functional equations of $L$-functions. We also present partial interpretability findings.

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Angelica Babei, François Charton, Edgar Costa, Xiaoyu Huang, Kyu-Hwan Lee, David Lowry-Duda, Ashvni Narayanan, Alexey Pozdnyakov. 2025-02-14. Learning Euler Factors of Elliptic Curves. https://arxiv.org/abs/2502.10357

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