Murmurations of elliptic curves

04/21/2022

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by   Yang-Hui He, et al.

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We investigate the average value of the pth 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.