{
  "id": 3699,
  "curve_key": "1143882651717116414585542924353:-1179929728571201645683562208058169130418661985",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-23830888577439925303865477591",
    "1365659408068526380967008026715318015465071"
  ],
  "rank_lower_bound": 10,
  "torsion": [
    4
  ],
  "naive_height": 207.6359433010417,
  "faltings_height": 15.226007901537564,
  "conductor": "2898874751395323625628640249570894",
  "bad_primes": [
    "2",
    "3",
    "7",
    "13",
    "17",
    "19",
    "29",
    "41",
    "79",
    "127",
    "503",
    "719",
    "1823",
    "3203",
    "4139",
    "7507"
  ],
  "discriminant": "60474035373840720764585582513008201747431479490337616287680365173087062571193468630784",
  "regulator": "1766168846041.514749112525598030497283895477423272269193855",
  "points": [
    [
      "112176888463691",
      "322458722065248047190"
    ],
    [
      "196780058095177643/1849",
      "14844143459752461270888138/79507"
    ],
    [
      "197156333848190579/3025",
      "49724460398598165849914082/166375"
    ],
    [
      "28517255250582945155/116281",
      "127080430442754867021929090502/39651821"
    ],
    [
      "1176604429085674503587/6806881",
      "27575849632554022051156653147726/17759152529"
    ],
    [
      "1507397277360757208203/8346321",
      "41434081354984450154097138198742/24112521369"
    ],
    [
      "6676796634583870757463/90573289",
      "84060052034613595371958631311034/861985991413"
    ],
    [
      "2242538432800383372378347/2098189636",
      "3324909101635308272956416735069514779/96109674466616"
    ],
    [
      "4095002777984111220139739/55031998921",
      "855415120030806202197295491972761670/12909901594878469"
    ],
    [
      "155934633840944574971056036155/1482158294418481",
      "8649217284132035388085580809182897924095078/57061329084582866089129"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Specialization at t = 1205/4264 of the Elkies-Klagsbrun Z/4 fibration E1: y^2 + a*xy + a*c*y = x^3 + c*x^2, a = (8t-1)(32t+7), c = 8(t+1)(15t-8)(31t-7) (arXiv:2003.00077, eq. (5)), found by searching small-height t = a/b for small conductor, with points from a 2-descent (PARI ellrank).",
  "created_at": "2026-09-30 01:45:38",
  "updated_at": "2026-09-30 01:45:38"
}