{
  "id": 336,
  "curve_key": "747003883046244014219126725033425:-20266078453621560514083513323000574183697419065625",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-15562580896796750296231806771530",
    "23456109321321254485649290545253053437231113097"
  ],
  "rank_lower_bound": 19,
  "torsion": [],
  "naive_height": 227.08086951938526,
  "faltings_height": 16.775502090662243,
  "conductor": "85455106033620726737244174703654827512709437318056845761537606762550",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "17",
    "19",
    "31",
    "41",
    "61",
    "3449",
    "394811",
    "795549335102805422537844157414441015295531368511"
  ],
  "discriminant": "3544726544965643121274669432217026701297680718000813558390880368205080304016057400950784000000",
  "regulator": "82887976042256042412.09408098706088009346633362934976932526983721497130669867",
  "points": [
    [
      "409691533901173609",
      "262219764785557112439941895"
    ],
    [
      "890231819944231696161/529",
      "26561553854378298458693996966465/12167"
    ],
    [
      "45567182897204134209",
      "-307594289422575186875851084505"
    ],
    [
      "63175870291011535660593/160801",
      "-15878337908118844106092342975151929/64481201"
    ],
    [
      "240896772069818642121/1849",
      "-3737228019675740945874754477355/79507"
    ],
    [
      "-1708229991390495",
      "212263697073716737861831"
    ],
    [
      "-813229246067344725579/573049",
      "89622493920158626179994036768855/433798093"
    ],
    [
      "429243338708761/9",
      "4069212689107427777096845/27"
    ],
    [
      "102095509464973527609/175561",
      "8889067560037020782074352027885/73560059"
    ],
    [
      "431214922555557681/289",
      "293022391856009204424854855/4913"
    ],
    [
      "27152520564440015160369/7134241",
      "2651099281776349889901270083461945/19055557711"
    ],
    [
      "4873010421309969",
      "251664694024185370945015"
    ],
    [
      "13649932583307609",
      "1534370343091861450195495"
    ],
    [
      "13945021565629920361/729",
      "51044619867771013294954990085/19683"
    ],
    [
      "-4635737253241708335/43681",
      "1446545720515270792335518544167/9129329"
    ],
    [
      "69001266790065441961201/1420864",
      "18067275787972871281115362781545435/1693669888"
    ],
    [
      "2084323733451793",
      "8590688171130949818871"
    ],
    [
      "13798057092247569",
      "1560668075628647535937015"
    ],
    [
      "626511991436294731238324505/20204063881",
      "15560532783894119034948542124787342243123/2871825844109221"
    ]
  ],
  "submitter": "7fff-zip",
  "commentary": "New in this search: Mestre quartic family with roots [0,115,206,234,731,784], T=14021/38. 19 independent rational points certified exactly by Cremona-Brumer quadratic characters; quartic point box [10000000,10000].",
  "created_at": "2026-08-24 19:18:38",
  "updated_at": "2026-08-24 19:18:38"
}