{
  "id": "1908.11088",
  "version": "v1",
  "published": "2019-08-29T08:17:14.000Z",
  "updated": "2019-08-29T08:17:14.000Z",
  "title": "Integrality properties in the Moduli Space of Elliptic Curves: Isogeny Case",
  "authors": [
    "Stefan Schmid"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "For a fixed $j$-invariant $j_0$ of an elliptic curve without complex multiplication we bound the number of $j$-invariants $j$ that are algebraic units and such that elliptic curves corresponding to $j$ and $j_0$ are isogenous. Our bounds are effective. We also modify the problem slightly by fixing a singular modulus $\\alpha$ and looking at all $j$ such that $j-\\alpha$ is an algebraic unit and such that elliptic curves corresponding to $j$ and $j_0$ are isogenous. The number of such $j$ can again be bounded effectively.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-08-29T08:17:14.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "moduli space",
      "isogeny case",
      "integrality properties",
      "algebraic unit",
      "elliptic curves corresponding"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}