We investigate the average value of the Frobenius trace at p over elliptic curves in a fixed conductor range with given rank. Plotting this average as p varies over the primes yields a striking oscillating pattern, the details of which vary with the rank. Based on this observation, we perform various data-scientific experiments with the goal of classifying elliptic curves according to their ranks.

翻译：我们研究了在给定秩的固定导子范围内，椭圆曲线上Frobenius迹在素数p处的平均值。将该平均值随素数p变化的关系绘制成图时，会产生显著的振荡模式，其具体形态随椭圆曲线的秩而变化。基于这一观测，我们开展了多种数据科学实验，旨在根据椭圆曲线的秩对其进行分类。