{
  "id": 379,
  "curve_key": "3129032084741790230730077743504:-5329758039325269491026637546694931105530611392",
  "ainvs": [
    "0",
    "1",
    "0",
    "-65188168432120629806876619656",
    "6168701434404225366706167935131419820676100"
  ],
  "rank_lower_bound": 16,
  "torsion": [],
  "naive_height": 210.65482952534342,
  "faltings_height": 15.479601128222768,
  "conductor": "68282354023300785772619028432224791293185377795283493596007917010323146498247760",
  "bad_primes": [
    "2",
    "3",
    "5",
    "4217",
    "1668800843",
    "434121897161",
    "93127391704528507822425138066232712382500786154827489"
  ],
  "discriminant": "1290241511271004191707961923166221344342817079498782404272214877293622872824010233676800",
  "regulator": "63155659086251644092.29757316779224019778613109220604430031059120748261",
  "points": [
    [
      "42643705047976",
      "1861822593558242821314"
    ],
    [
      "238797775927693966/3025",
      "-204756068733769879759046436/166375"
    ],
    [
      "8029587091655936185486/42758521",
      "-207244466929221062956033953828204/279597968819"
    ],
    [
      "1425506870602466968/24649",
      "-6230584840984518637099875990/3869893"
    ],
    [
      "3164543384461497841093/13380964",
      "-97640985595677382828093341762945/48947566312"
    ],
    [
      "389627999234101464/49",
      "243082620369847899916606542/343"
    ],
    [
      "1509963285868529436037/14092516",
      "34043600318210567335294432312095/52903305064"
    ],
    [
      "737872554448006258/2809",
      "398657546354987882224895280/148877"
    ],
    [
      "10783717700263113088954/88266025",
      "138892374250195278556652448691008/829259304875"
    ],
    [
      "-55606432458312203/196",
      "-3709666914505144816617255/2744"
    ],
    [
      "9601416973505883444592/22477081",
      "-799351373754977420530017591822630/106563841021"
    ],
    [
      "98915181169395041900731/194797849",
      "27725879017144902216344899198170288/2718793578493"
    ],
    [
      "973553471278024",
      "-29418441614876879456766"
    ],
    [
      "-2068244305090676384/7921",
      "-1636386961089461615445648594/704969"
    ],
    [
      "3241023954396001/16",
      "-72282225395532125218041/64"
    ],
    [
      "21709413616569222616/117649",
      "26242475189114479645988099538/40353607"
    ]
  ],
  "submitter": "Christopher R. Hill",
  "commentary": "Found with Rank Hunter v0.8.5; family=Fermigier--Mestre K3, arithmetic generic rank = 12; parameter=3187/6; local status: rigorous rank lower bound >= 16.",
  "created_at": "2026-08-27 01:36:07",
  "updated_at": "2026-08-27 01:36:07"
}