Murmurations of elliptic curves
arXiv:2204.10140 · doi:10.1080/10586458.2024.2382361
Abstract
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.
27 pages, 16 figures, 2 tables