Learning Euler Factors of Elliptic Curves

2025/02/14 by Babei, Angelica, Charton, François, Costa, Edgar +5 · 4 citations
#FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2502.10357

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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