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 mathbbQ and evaluate and interpret their predictive capacity. In keeping with similar experiments by Kazalicki--Vlah, Bujanovi'c--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 saliency, murmurations and Mestre--Nagao sums.