{
  "id": 3657,
  "curve_key": "663909359684953:-17104264495877590059869",
  "ainvs": [
    "1",
    "1",
    "0",
    "-13831444993436",
    "19796596662682167156"
  ],
  "rank_lower_bound": 6,
  "torsion": [
    4
  ],
  "naive_height": 102.38750024876568,
  "faltings_height": 6.23749483159222,
  "conductor": "157438656284322",
  "bad_primes": [
    "2",
    "3",
    "7",
    "29",
    "83",
    "109",
    "113",
    "227",
    "557"
  ],
  "discriminant": "45837710009179953159003938550570545772",
  "regulator": "11907304.350658803604013575070193348314761678267785",
  "points": [
    [
      "24682172839/11236",
      "135665313690287/1191016"
    ],
    [
      "332990925651/46225",
      "170366757305903556/9938375"
    ],
    [
      "17495910109177/3775249",
      "54497163131474737087/7335308807"
    ],
    [
      "62866385506261/28976689",
      "3483770290682607759/155981516887"
    ],
    [
      "343160639128774/95746225",
      "3776501019322482219348/936876811625"
    ],
    [
      "11606123351932840/5569786161",
      "62592102278530298182766/415678710981591"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Specialization at t = -791/872 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": "2026-09-29 19:28:08",
  "updated_at": "2026-09-29 19:28:08"
}