{
  "id": "2408.04159",
  "version": "v1",
  "published": "2024-08-08T02:04:20.000Z",
  "updated": "2024-08-08T02:04:20.000Z",
  "title": "Models of CM elliptic curves with a prescribed $\\ell$-adic Galois image",
  "authors": [
    "Enrique González-Jiménez",
    "Álvaro Lozano-Robledo",
    "Benjamin York"
  ],
  "comment": "38 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "For each prime number $\\ell$ and for each imaginary quadratic order of class number one or two, we determine all the possible $\\ell$-adic Galois representations that occur for any elliptic curve with complex multiplication by such an order over its minimal field of definition, and then we determine all the isomorphism classes of elliptic curves that have a prescribed $\\ell$-adic Galois representation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-08-08T02:04:20.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G05",
      "11G15",
      "14H52",
      "14K22"
    ],
    "keywords": [
      "cm elliptic curves",
      "adic galois image",
      "adic galois representation",
      "imaginary quadratic order",
      "prime number"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 38,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}