Learning Euler Factors of Elliptic Curves
This work addresses a specific challenge in computational number theory by applying machine learning to elliptic curve data, representing an incremental advancement in the domain.
The paper tackled the problem of predicting Frobenius traces of elliptic curves using transformer and neural network models, achieving high accuracy without relying on traditional number-theoretic tools.
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.