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.

翻译：我们应用一维卷积神经网络对$\mathbb{Q}$上椭圆曲线的Frobenius迹进行建模，评估并解释其预测能力。与Kazalicki--Vlah、Bujanović--Kazalicki--Novak及Pozdnyakov等类似实验一致，观察到该方法在广范围导子区间内对解析秩具有高精度预测。通过显著性曲线解读预测结果，并探索簇群振动与Mestre--Nagao和之间有趣的相互作用——这种相互作用的细节随导子与（预测）秩的变化而呈现差异。