Learning Euler Factors of Elliptic Curves

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 $a_p\mathrm{mod}2$ from $a_q\mathrm{mod}2$, and cross-analysis such as $a_p\mathrm{mod}2$ 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.

18 pages