Murmurations, Mestre--Nagao sums, and Convolutional Neural Networks for elliptic curves

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.