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Murmurations of elliptic curves

Experimental Mathematics (Exp. Math.), 2022
Abstract

We investigate the average value of the ppth 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.

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