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Murmurations of elliptic curves
- Source :
- Experimental Mathematics, 2024
- Publication Year :
- 2022
-
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.<br />Comment: 27 pages, 16 figures, 2 tables
Details
- Database :
- arXiv
- Journal :
- Experimental Mathematics, 2024
- Publication Type :
- Report
- Accession number :
- edsarx.2204.10140
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1080/10586458.2024.2382361