Murmurations of elliptic curves
Murmurations of elliptic curves
Murmurations of elliptic curves
Murmurations of elliptic curves
Murmurations of elliptic curves
Murmurations of elliptic curves
Murmurations of elliptic curves
Murmurations of elliptic curves
Murmurations of elliptic curves
Murmurations of elliptic curves
Murmurations of elliptic curves
Murmurations of elliptic curves
Murmurations of elliptic curves
Murmurations of elliptic curves
Murmurations of elliptic curves
Murmurations of elliptic curves

Murmuring elliptic curves

The average p-th Dirichlet coefficients of elliptic curves (p prime) are found to oscillate dramatically in a fixed conductor range with a given rank.

Murmurations of elliptic curves

Arxiv

Y. He, K. Lee, T. Oliver, A. Pozdnyakov

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.

Arxiv

Y. He, K. Lee, T. Oliver, A. Pozdnyakov