{
  "id": "1604.07774",
  "version": "v1",
  "published": "2016-04-26T18:02:49.000Z",
  "updated": "2016-04-26T18:02:49.000Z",
  "title": "Eta quotients, Eisenstein series and Elliptic Curves",
  "authors": [
    "Ayse Alaca",
    "Saban Alaca",
    "Zafer Selcuk Aygin"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "We express all the newforms of weight $2$ and levels $30$, $33$, $35$, $38$, $40$, $42$, $44$, $45$ as linear combinations of eta quotients and Eisenstein series, and list their corresponding strong Weil curves. Let $p$ denote a prime and $E (\\zz_p)$ denote the the group of algebraic points of an elliptic curve $E$ over $\\zz_p$. We give a generating function for the order of $E (\\zz_p)$ for certain strong Weil curves in terms of eta quotients and Eisenstein series. We then use our generating functions to deduce congruence relations for the order of $E (\\zz_p)$ for those strong Weil curves.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-04-26T18:02:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F11",
      "11F20",
      "11F30",
      "11G07",
      "11Y35",
      "14H52"
    ],
    "keywords": [
      "eisenstein series",
      "eta quotients",
      "elliptic curve",
      "corresponding strong weil curves",
      "generating function"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160407774A"
    }
  }
}