{
  "id": 331,
  "curve_key": "948763191167997782038383786841:-804130320320662711789028864823969527325116765",
  "ainvs": [
    "1",
    "1",
    "0",
    "-19765899815999953792466328892",
    "930706389260018051001267482454403054915180"
  ],
  "rank_lower_bound": 19,
  "torsion": [],
  "naive_height": 207.07487022956042,
  "faltings_height": 15.243208785818325,
  "conductor": "3793516941765244041911805984731101725684082461834129521696000864322",
  "bad_primes": [
    "2",
    "3",
    "7",
    "11",
    "17",
    "19",
    "23",
    "41",
    "12348031756441",
    "62795042146961",
    "34766641820972554344399273084379"
  ],
  "discriminant": "120026114450375268731550080313050637490976047007792951958607127362398246018745515426132",
  "regulator": "1667257467816680568.761756590183763270982336299364955494250659404531856245151",
  "points": [
    [
      "8948871752189262/169",
      "-396291749135598048872560/2197"
    ],
    [
      "331631657273881498561/6538249",
      "-4048336062850691996481244470539/16718302693"
    ],
    [
      "734498777347765/16",
      "-22176824792338565475755/64"
    ],
    [
      "729780904227973/16",
      "-22541019394000164821987/64"
    ],
    [
      "24541525333748266947/605284",
      "-208450745296992975096570371071/470910952"
    ],
    [
      "387922489046025282919/2647129",
      "4680871983970916113209065564635/4306878883"
    ],
    [
      "272857891108108",
      "3981467493175044681502"
    ],
    [
      "128187235733585194/225",
      "44594835273094520808275792/3375"
    ],
    [
      "2825658530774346123631/2356225",
      "-149208357924334609825389518668201/3616805375"
    ],
    [
      "21723276711930582382/26569",
      "-99827762782453171410618564176/4330747"
    ],
    [
      "-9462795346882829837/203401",
      "121337901129172690209953839300/91733851"
    ],
    [
      "-16080994413244107/6889",
      "565124956676911235549761142/571787"
    ],
    [
      "1953541393275260017/38809",
      "1923397946333882434451317325/7645373"
    ],
    [
      "117390910883342715/2116",
      "6804564761696889034824215/97336"
    ],
    [
      "29165334153265143781563223/521672508361",
      "-7469235222751949106574169084939264627/376787880941391109"
    ],
    [
      "67188964108724004991/1216609",
      "-116559474111350125762347666616/1341919727"
    ],
    [
      "107294547606315080210/677329",
      "742589868815121423327651929090/557441767"
    ],
    [
      "89023261784394761389/4669921",
      "7557559331086612408945520058817/10091699281"
    ],
    [
      "417649578592662",
      "8094849481736481648416"
    ]
  ],
  "submitter": "7fff-zip",
  "commentary": "New in this search: Mestre quartic family with roots [0,115,206,234,731,784], T=9636/23. 19 independent rational points certified exactly by Cremona-Brumer quadratic characters; quartic point box [10000000,10000].",
  "created_at": "2026-08-24 19:17:47",
  "updated_at": "2026-08-24 19:17:47"
}