We investigate the average value of the $p$th Dirichlet coefficients of elliptic curves for a prime p in a fixed conductor range with given rank. Plotting this average 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：我们调查了在固定航程范围内,按给定军衔排列的优等离子体等离子体等离子体离子体曲线平均值。 绘制这一平均数会产生惊人的振动模式, 其细节随军衔的不同而不同。 基于这一观察, 我们进行了各种数据科学实验, 目的是根据他们的军衔对离子体曲线进行分类 。