{
  "id": 6325,
  "curve_key": "334874272536978018211809:-192340189724240099143832832819645777",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-6976547344520375379413",
    "222615960330725733067418094793517"
  ],
  "rank_lower_bound": 19,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 162.50412632518618,
  "faltings_height": 11.394604915946555,
  "conductor": "4637348626603819798729925535184163156289342630775113693630",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "7291601",
    "1009499948760097960050619391414070412273697609501"
  ],
  "discriminant": "323097805367422872684118152615864792221621117540289265371735244800",
  "regulator": "163932328197032372.7002964083574563461357820806784836537778205314963624853209",
  "points": [
    [
      "32618208783",
      "5455031407746928"
    ],
    [
      "15737604063",
      "10803676096764208"
    ],
    [
      "-45514053537",
      "-21115450827630992"
    ],
    [
      "51942821583",
      "615672707506288"
    ],
    [
      "38825628015",
      "3205291974041248"
    ],
    [
      "44595435783",
      "-427916155105712"
    ],
    [
      "51935375775",
      "608884450337968"
    ],
    [
      "98813984583",
      "22317553007969128"
    ],
    [
      "72436152207",
      "-9865832004591248"
    ],
    [
      "71690372463",
      "9535058978831008"
    ],
    [
      "44779332207",
      "-42862446321248"
    ],
    [
      "-33257727537",
      "20441505864131008"
    ],
    [
      "166837090143",
      "60848213312969008"
    ],
    [
      "58734565567",
      "-3933348959888208"
    ],
    [
      "24151786563",
      "-8258815101528272"
    ],
    [
      "75996795993",
      "11460380770417348"
    ],
    [
      "384015395343",
      "-232752053554977152"
    ],
    [
      "402215031895/9",
      "-8019310747530544/27"
    ],
    [
      "1073690774439/25",
      "-185687319120668848/125"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Source attribution: Layr-Labs elliptic-rank-challenge-public, submission/board/1-19-mestre-11010011.ec, commit 287daf3c0197665eadddf883b1d165a52296433d.\r\n\r\nOwn find: Mestre ten-root construction using quickrank quartic points and the Washington map, roots [0,2,4,28,56,61,64,81,96,108]. The source supplies 19 rational points and marks CLAIM rank=19. This is a Layr-Labs result.",
  "created_at": "2026-11-01 00:46:45",
  "updated_at": "2026-11-01 00:46:45"
}