{
  "id": "1007.2306",
  "version": "v3",
  "published": "2010-07-14T12:13:10.000Z",
  "updated": "2013-03-06T09:35:10.000Z",
  "title": "$y$-coordinates of elliptic curves",
  "authors": [
    "Ja Kyung Koo",
    "Dong Hwa Shin"
  ],
  "comment": "We changed its title and shortened its contents",
  "categories": [
    "math.NT"
  ],
  "abstract": "By a change of variables we obtain new $y$-coordinates of elliptic curves. Utilizing these $y$-coordinates as modular functions, together with the elliptic modular function, we generate the modular function fields of level $N\\geq3$. Furthermore, by means of the singular values of the $y$-coordinates we construct the ray class fields modulo $N$ over imaginary quadratic fields as well as normal bases of these ray class fields.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2013-03-06T09:35:10.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F11",
      "11G15",
      "11R37"
    ],
    "keywords": [
      "elliptic curves",
      "coordinates",
      "ray class fields modulo",
      "modular function fields",
      "imaginary quadratic fields"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1007.2306K"
    }
  }
}