{
  "id": 334,
  "curve_key": "964226818517201392511168166825:-914722908399539232586664110119267352073983125",
  "ainvs": [
    "1",
    "-1",
    "0",
    "-20088058719108362343982670142",
    "1058707069906879133804800274913812097605016"
  ],
  "rank_lower_bound": 19,
  "torsion": [],
  "naive_height": 207.12337220007583,
  "faltings_height": 15.181046402326983,
  "conductor": "4645654301378334775416336624703209894193008406665345269653301849346150",
  "bad_primes": [
    "2",
    "3",
    "5",
    "13",
    "31",
    "53",
    "73",
    "511982641",
    "33062977231",
    "113353501142719",
    "3450630579549091047282711829"
  ],
  "discriminant": "34580924922872053571701566010054140579738463663558732474684969795750563761232693187500",
  "regulator": "62907649343052817485.60738489546805567900143908991350939103672986355899666704",
  "points": [
    [
      "10508859682607163",
      "-1077194402470961252875491"
    ],
    [
      "1306578693049494",
      "-46960996436311739108772"
    ],
    [
      "612662279994124",
      "-14789097770206369260612"
    ],
    [
      "-5926627722346818141/4813636",
      "10992890250054193839950098105377/10561117384"
    ],
    [
      "67809425786269",
      "91340535227206609553"
    ],
    [
      "66171076936014",
      "-138549750679457517282"
    ],
    [
      "58198476681330",
      "-294507315659386444224"
    ],
    [
      "258844710229899531/1849",
      "79110808276044753053458071/79507"
    ],
    [
      "540593268632382099/2401",
      "331714850451843238145651712/117649"
    ],
    [
      "501455703792639",
      "10820369197059447709893"
    ],
    [
      "31967357275729324105/59049",
      "175062045796321834905628510898/14348907"
    ],
    [
      "9566512359620240160879/51566761",
      "713911854210074815335753692965188/370300910741"
    ],
    [
      "1110770293379349874",
      "1170675099301436955861820238"
    ],
    [
      "274850537550015",
      "4037384841201267216636"
    ],
    [
      "730138840811274",
      "-19381193367213954467112"
    ],
    [
      "3731969799604017021/55225",
      "-1285624425785137175703469074/12977875"
    ],
    [
      "56854032117244",
      "-316849875652479180972"
    ],
    [
      "831128595891639653442999/16387584196",
      "-865867845122614673376815589482897043/2097840203266744"
    ],
    [
      "186814718475324298539/4541161",
      "5317559327289518776055812906383/9677214091"
    ]
  ],
  "submitter": "7fff-zip",
  "commentary": "New in this search: Mestre quartic family with roots [0,115,206,234,731,784], T=2194/13. 19 independent rational points certified exactly by Cremona-Brumer quadratic characters; quartic point box [10000000,10000].",
  "created_at": "2026-08-24 19:18:27",
  "updated_at": "2026-08-24 19:18:27"
}