{
  "id": 1086,
  "curve_key": "1020109278751334339505975322425:-810974180829898480594824551594730035632438125",
  "ainvs": [
    "1",
    "-1",
    "0",
    "-21252276640652798739707819217",
    "938627524108684110053910801619511357084941"
  ],
  "rank_lower_bound": 11,
  "torsion": [
    2,
    2
  ],
  "naive_height": 207.29238764222885,
  "faltings_height": 15.286094242586989,
  "conductor": "169865982816721595689011110169981949651950",
  "bad_primes": [
    "2",
    "3",
    "5",
    "13",
    "29",
    "37",
    "53",
    "59",
    "79",
    "103",
    "163",
    "241",
    "257",
    "463",
    "557",
    "757",
    "1481",
    "2287",
    "159319"
  ],
  "discriminant": "233721062158155126934574324579450269809917179389909971086488059245472324281724300250000",
  "regulator": "117834128118.030247451542313326655324237223950139480060116964",
  "points": [
    [
      "19017299960234",
      "735761064017992960283"
    ],
    [
      "139834465497809",
      "837319973368878505283"
    ],
    [
      "3252657614678",
      "932488902903515289863"
    ],
    [
      "12675419128250",
      "819318321492432776771"
    ],
    [
      "44878398411779",
      "274313029862925460148"
    ],
    [
      "222075911530490",
      "2677925266366399108499"
    ],
    [
      "-48164331466741",
      "-1360329887527677896767"
    ],
    [
      "257065481913530",
      "3530293363328357073251"
    ],
    [
      "46090868872710",
      "238758440802567342931"
    ],
    [
      "-163796334743607",
      "-158560586391641489941"
    ],
    [
      "1768050577343369967/12769",
      "1163867358320331630990007181/1442897"
    ]
  ],
  "submitter": "dujella",
  "history": [],
  "commentary": "found by Dujella - Peral (2019), induced by the rational Diophantine triple {21409906185/74591676404, −31580198976/18647919101, −10309975195/18647919101}",
  "created_at": "2026-09-23 17:56:38",
  "updated_at": "2026-09-23 17:56:38"
}