{
  "id": 337,
  "curve_key": "7788877428888587018305319002861249:-361104193906175225561648160057369979967543633935393",
  "ainvs": [
    "1",
    "0",
    "0",
    "-162268279768512229548027479226276",
    "417944668872887979025847241579270199663848529680"
  ],
  "rank_lower_bound": 19,
  "torsion": [],
  "naive_height": 234.1140144425401,
  "faltings_height": 17.558370639230308,
  "conductor": "42591546162844993850851508738322575321783987912035384306194523783699590",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "13",
    "17",
    "19",
    "23",
    "31",
    "43",
    "157",
    "1019",
    "44249",
    "460589",
    "28217543",
    "27038992544935731914128602109293389"
  ],
  "discriminant": "197991066515791420644080408315411349123160046175556275120584559630465306544722943095166864250265600",
  "regulator": "2334351474430798085.826291464877663755778312160887020417773538122218770317579",
  "points": [
    [
      "3404128207829471448",
      "-6280667815176558207747997284"
    ],
    [
      "2019237841998067848",
      "-2869277706439965574463152164"
    ],
    [
      "4003885097932168432/9",
      "-8008392140607804427928828428/27"
    ],
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      "-6837631768653672",
      "1098996906036260592329676"
    ],
    [
      "377771325502728",
      "597242226991339938325596"
    ],
    [
      "1301581383017930",
      "457104280931338878158600"
    ],
    [
      "2375698019031780",
      "-214132057902391665984240"
    ],
    [
      "15074541312221640096/1225",
      "22872483220024242041000638764/42875"
    ],
    [
      "134167592165328562/9",
      "30925104798017596474014232/27"
    ],
    [
      "208133112480715498356/12769",
      "2092767663218217876382096470732/1442897"
    ],
    [
      "63867824944237878",
      "15829636965653541388717176"
    ],
    [
      "28074782029842938558867592/434013889",
      "145960227219834149035930958532697005852/9041811349537"
    ],
    [
      "-4906247057172370",
      "1046887479457944458658680"
    ],
    [
      "61965565735548780871982898/2772127801",
      "411782275448622558381105958744685838786/145955300850451"
    ],
    [
      "-684523190213992",
      "727117818176270670094796"
    ],
    [
      "245274189561110718911689320/1158245089",
      "3834424479051508503075678346500684112860/39418555113937"
    ],
    [
      "89223780640476173867088/2825761",
      "24578915930607842272732643125222236/4750104241"
    ],
    [
      "82864824052009721736",
      "754319463202526821026476070300"
    ],
    [
      "134328903237790271574/4489",
      "1422122018123538358094814731862/300763"
    ]
  ],
  "submitter": "7fff-zip",
  "commentary": "New in this search: Mestre quartic family with roots [0,44,53,78,525,534], T=8551/46. 19 independent rational points certified exactly by Cremona-Brumer quadratic characters; quartic point box [10000000,10000].",
  "created_at": "2026-08-24 19:18:42",
  "updated_at": "2026-08-24 19:18:42"
}