{
  "id": "1705.07514",
  "version": "v1",
  "published": "2017-05-21T22:09:31.000Z",
  "updated": "2017-05-21T22:09:31.000Z",
  "title": "A method for construction of rational points over elliptic curves",
  "authors": [
    "Kirti Joshi"
  ],
  "comment": "6 pages",
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "I provide a systematic construction of points (defined over number fields) on Legendre elliptic curves over $\\mathbb{Q}$: for any odd integer $n\\geq 3$ my method constructs $n$ points on the Legendre curve and I show that rank of the subgroup of the Mordell-Weil group they generate is $n$ if $n\\geq 7$. I also show that every elliptic curve over any number field admits similar type of points after a finite base extension.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-05-21T22:09:31.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "rational points",
      "number field admits similar type",
      "construction",
      "legendre elliptic curves",
      "finite base extension"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}