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Experimental Mathematics
Article . 2024 . Peer-reviewed
License: CC BY
Data sources: Crossref
image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/
arXiv.org e-Print Archive
Preprint . 2022
Data sources: arXiv.org e-Print Archive
https://dx.doi.org/10.48550/ar...
Article . 2022
License: arXiv Non-Exclusive Distribution
Data sources: Datacite
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Murmurations of Elliptic Curves

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 04 Aug 2024Embargo end date: 01 Jan 2022 English Publisher:Informa UK LimitedJournal:Experimental Mathematics, volume 34, pages 528-540 (issn: 1058-6458, eissn: 1944-950X, Copyright policy )
Authors: He, Yang-Hui; Lee, Kyu-Hwan; Oliver, Thomas; Pozdnyakov, Alexey;

doi: 10.1080/10586458.2024.2382361 , 10.48550/arxiv.2204.10140

arXiv: http://arxiv.org/abs/2204.10140

Murmurations of Elliptic Curves

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

Related Organizations
Keywords

High Energy Physics - Theory, FOS: Computer and information sciences, Mathematics - Number Theory, High Energy Physics - Theory (hep-th), Statistics - Machine Learning, FOS: Mathematics, FOS: Physical sciences, Machine Learning (stat.ML), Number Theory (math.NT)

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    This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
    		 4
    popularity
    This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
    		 Top 10%
    influence
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    		 Top 10%
    impulse
    This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
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citations
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
4
Top 10%
Top 10%
Average
Green
hybrid