{
  "id": 3523,
  "curve_key": "4424054864576177197752730370902801:-292230205101347654685069042544193559216438231071225",
  "ainvs": [
    "1",
    "1",
    "1",
    "-92167809678670358286515216060475",
    "338229404052485673037798099794982148230278297801"
  ],
  "rank_lower_bound": 16,
  "torsion": [
    2
  ],
  "naive_height": 232.4170942035706,
  "faltings_height": 17.21735243469797,
  "conductor": "1789399932124511774089607156478992325365460369832460586",
  "bad_primes": [
    "2",
    "3",
    "7",
    "11",
    "23",
    "43",
    "53",
    "71",
    "101",
    "107",
    "113",
    "193",
    "283",
    "491",
    "509",
    "1361",
    "2287",
    "4057",
    "6899",
    "23857",
    "49157",
    "611071"
  ],
  "discriminant": "688811158542019060834308601091705462064656657898351677864385828264770040417445265052875828232192",
  "regulator": "216578685366554.5002217442841867788528887379853764341766208979415800566",
  "points": [
    [
      "443143539999749670363/85849",
      "-72745942040543879618437410962/25153757"
    ],
    [
      "7683033234179123",
      "289176111134034933330342"
    ],
    [
      "111427202957698098067/28561",
      "-941288747494181466140939572714/4826809"
    ],
    [
      "211134308963918142278192957/60620348944",
      "-3639733087892304426696556003166849760543/14925457354200128"
    ],
    [
      "-686424451074385512583906717/160726422649",
      "-52108254452324127920658722732348593910358/64436347924942643"
    ],
    [
      "-72039890365665648053162529781738565/6575750750747283561",
      "3067488307779126029071343346528048105480141473971438/16862346715835027925643344309"
    ],
    [
      "3282468953710899",
      "-266568432297571746267226"
    ],
    [
      "7841507243963059",
      "312511028198727514754726"
    ],
    [
      "2370469800236743",
      "-364785370529246516195218"
    ],
    [
      "8212828764512863",
      "367737449315595962025122"
    ],
    [
      "8106438902390803",
      "351832431936800009900294"
    ],
    [
      "5016187740162727",
      "-46004159958795810841942"
    ],
    [
      "8434241125764659",
      "401055628700939056792614"
    ],
    [
      "6486068728963567",
      "115263387029161214540594"
    ],
    [
      "-362820708133781921111261/197993041",
      "-1971886401813430315798162075338262966/2785960079911"
    ],
    [
      "2100041037976153988418011467/90113435721",
      "-89091447691632383533639508887120783562498/27051062155651269"
    ]
  ],
  "submitter": "Alvaro Lozano-Robledo",
  "history": [],
  "commentary": "Rank exactly 16, torsion Z/2Z. Specialization at T = −1247/882 of the rank-9 fibration of X400 with a 2-torsion point (Li, 2026), and its 2-isogeny pair.",
  "created_at": "2026-09-27 19:17:11",
  "updated_at": "2026-09-27 19:17:11"
}