{
  "id": "1511.05108",
  "version": "v1",
  "published": "2015-11-16T20:01:33.000Z",
  "updated": "2015-11-16T20:01:33.000Z",
  "title": "Computing all elliptic curves over an arbitrary number field with prescribed primes of bad reduction",
  "authors": [
    "Angelos Koutsianas"
  ],
  "comment": "19 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "In this paper we study the problem of how to determine all elliptic curves defined over an arbitrary number field $K$ with good reduction outside a given finite set of primes $S$ of $K$ by solving $S$-unit equations. We give examples of elliptic curves over $\\mathbb Q$ and quadratic fields.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-11-16T20:01:33.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "arbitrary number field",
      "elliptic curves",
      "bad reduction",
      "prescribed primes",
      "quadratic fields"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv151105108K"
    }
  }
}