{
  "id": 4257,
  "curve_key": "13491686278211401727363236921:-1563376474113874682064248764652285109999725",
  "ainvs": [
    "1",
    "1",
    "0",
    "-281076797462737535986734102",
    "1809463511705756359279122892522372552920"
  ],
  "rank_lower_bound": 14,
  "torsion": [
    2
  ],
  "naive_height": 194.3156135260142,
  "faltings_height": 13.999122653147708,
  "conductor": "311560278166741566302026290678974420505803313066",
  "bad_primes": [
    "2",
    "3",
    "11",
    "13",
    "19",
    "31",
    "59",
    "67",
    "89",
    "97",
    "107",
    "163",
    "173",
    "467",
    "5209",
    "5563",
    "384751",
    "566173",
    "2031067"
  ],
  "discriminant": "6762888600989447475499152769013148703872694934096024202673820122626608957947212",
  "regulator": "1601310897469784.56804067367687244706682997181647939596340914981402",
  "points": [
    [
      "-54580233026337/4",
      "445725131224368435471/8"
    ],
    [
      "-11228545134402",
      "59580619171889922690"
    ],
    [
      "633973247598",
      "40392117100145095440"
    ],
    [
      "13633364485931/4",
      "238803924015930560097/8"
    ],
    [
      "58056306834859/4",
      "224485960222295378417/8"
    ],
    [
      "16623128437749",
      "41599634417056381392"
    ],
    [
      "-27266817278144103684/3308761",
      "359414998087732963406556386940/6018636259"
    ],
    [
      "-689005390784717/36",
      "2884388787011578212527/216"
    ],
    [
      "26136625872186/25",
      "4868184654943944776226/125"
    ],
    [
      "251627370729564/25",
      "29243934411713088852/125"
    ],
    [
      "35071070909986002/1369",
      "5413358258681145476633730/50653"
    ],
    [
      "416171998921244460/57121",
      "166276641579592681009604100/13651919"
    ],
    [
      "15685164155695925454/3301489",
      "144634757112202005160365367632/5998805513"
    ],
    [
      "23816802130887971693/769129",
      "101848003554651242357347987191/674526133"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Found by specializing the family associated with curve#802 at T = -334/279. The original PARI/GP computation returned rank bounds [14,14]. Fourteen rational points are supplied.",
  "created_at": "2026-10-15 20:36:51",
  "updated_at": "2026-10-15 20:36:51"
}