{
  "id": "1407.7892",
  "version": "v2",
  "published": "2014-07-29T21:27:10.000Z",
  "updated": "2016-01-15T20:00:07.000Z",
  "title": "Picard curves over Q with good reduction away from 3",
  "authors": [
    "Beth Malmskog",
    "Christopher Rasmussen"
  ],
  "comment": "27 pages; A previous lemma was incorrect and has been removed; Corrected computation has identified 18 new such curves (63 in total)",
  "categories": [
    "math.NT"
  ],
  "abstract": "Inspired by methods of N. P. Smart, we describe an algorithm to determine all Picard curves over Q with good reduction away from 3, up to Q-isomorphism. A correspondence between the isomorphism classes of such curves and certain quintic binary forms possessing a rational linear factor is established. An exhaustive list of integral models is determined, and an application to a question of Ihara is discussed.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-07-29T21:27:10.000Z",
      "comment": "27 pages",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2016-01-15T20:00:07.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11E76",
      "11G30",
      "11J86",
      "11Y40",
      "14Q05",
      "14H30",
      "11G32"
    ],
    "keywords": [
      "reduction away",
      "picard curves",
      "rational linear factor",
      "quintic binary forms possessing",
      "integral models"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1407.7892M"
    }
  }
}