Murmurations of elliptic curves

Yang-Hui He, Kyu-Hwan Lee, Thomas Oliver, Alexey Pozdnyakov

Published 2022-04-21Version 1

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.