{
  "id": "2204.10140",
  "version": "v1",
  "published": "2022-04-21T14:45:40.000Z",
  "updated": "2022-04-21T14:45:40.000Z",
  "title": "Murmurations of elliptic curves",
  "authors": [
    "Yang-Hui He",
    "Kyu-Hwan Lee",
    "Thomas Oliver",
    "Alexey Pozdnyakov"
  ],
  "comment": "25 pages, 16 figures, 2 tables",
  "categories": [
    "math.NT",
    "hep-th",
    "stat.ML"
  ],
  "abstract": "We investigate the average value of the $p$th 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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-04-21T14:45:40.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "murmurations",
      "th dirichlet coefficients",
      "data-scientific experiments",
      "average yields",
      "classifying elliptic curves"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}