{
  "id": 6324,
  "curve_key": "75504337655723247137481:-19343292298660607248594838142509445",
  "ainvs": [
    "1",
    "-1",
    "0",
    "-1573007034494234315364",
    "22388069790509695333386102725264"
  ],
  "rank_lower_bound": 19,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 158.0354311796199,
  "faltings_height": 11.123959622261316,
  "conductor": "546321491073191762170183455262948859623343119820126508531642",
  "bad_primes": [
    "2",
    "3",
    "23",
    "1319617128196115367560829602084417535322084830483397363603"
  ],
  "discriminant": "32569502011819400093537656868955959215305223431196661932622369472",
  "regulator": "638955495209250275.1260859313699026557841471703638317064654152771169677031358",
  "points": [
    [
      "17845269088",
      "15046999892620"
    ],
    [
      "17833573312",
      "-86367780976652"
    ],
    [
      "28069188976",
      "591740136070924"
    ],
    [
      "-5080222688",
      "5499837270576340"
    ],
    [
      "58851566128",
      "-11560606567717820"
    ],
    [
      "-44943439232",
      "1517451488370892"
    ],
    [
      "17814310651",
      "139272536479774"
    ],
    [
      "30036943603",
      "1496519919580567"
    ],
    [
      "9890948191",
      "2792337912684655"
    ],
    [
      "9507438325",
      "2879612048733808"
    ],
    [
      "9424644535",
      "-2898309657448598"
    ],
    [
      "8083444201",
      "-3193895739539501"
    ],
    [
      "-1539165803",
      "4980517017303643"
    ],
    [
      "16858241320",
      "-813061227007388"
    ],
    [
      "156700233184",
      "60196814768338828"
    ],
    [
      "63734692057",
      "13454719810659955"
    ],
    [
      "27635657537",
      "-152181027628452"
    ],
    [
      "-13901283872",
      "6447372604151692"
    ],
    [
      "2161649383",
      "-4358656940680358"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Source attribution: Layr-Labs elliptic-rank-challenge-public, submission/board/1-19-m10-kh-b1.ec, commit 587264a497665705f4236787ba4c1a395556957d.\r\n\r\nOwn find from the kshitij-hash lane: Mestre ten-root construction, roots [0,10,12,31,47,48,58,59,72,95]. The source supplies 19 rational points and states certified rank 19. This is a Layr-Labs source result.",
  "created_at": "2026-11-01 00:44:24",
  "updated_at": "2026-11-01 00:44:24"
}