{
  "id": 6322,
  "curve_key": "109049299205261138752:-1085041334486553707849856799616",
  "ainvs": [
    "0",
    "-1",
    "0",
    "-2271860400109607057",
    "1255834878635242480418314389"
  ],
  "rank_lower_bound": 18,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 138.41499522047445,
  "faltings_height": 9.471232606509599,
  "conductor": "12206752206633277112823808078320329393984262664730856",
  "bad_primes": [
    "2",
    "3",
    "59",
    "617",
    "779410038591460709",
    "17926095928214758492312456897"
  ],
  "discriminant": "69139044498370881567034048955606345687526863733035568384",
  "regulator": "9402440317301042.0806125558654880596554059151517566420512978882417414183877",
  "points": [
    [
      "1068037439",
      "6907782708858"
    ],
    [
      "549475583",
      "13168242315834"
    ],
    [
      "521239127",
      "-14603695551102"
    ],
    [
      "1501895237",
      "35093412238458"
    ],
    [
      "-1087091551",
      "-49405111796862"
    ],
    [
      "232181017",
      "-27218898588862"
    ],
    [
      "201425143",
      "28397135617886"
    ],
    [
      "1396394564",
      "-28394998675233"
    ],
    [
      "692150740",
      "-3867235200647"
    ],
    [
      "-999041603",
      "-50283102229882"
    ],
    [
      "-1387730063",
      "41666300699842"
    ],
    [
      "1164178588",
      "-13740764331949"
    ],
    [
      "4007441039",
      "237716896692342"
    ],
    [
      "2210740412",
      "83893114440867"
    ],
    [
      "700184417",
      "-2895650670462"
    ],
    [
      "688665665",
      "4229595418878"
    ],
    [
      "1703416901/4",
      "152961792288291/8"
    ],
    [
      "211137407",
      "-28028065578822"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Source attribution: Layr-Labs elliptic-rank-challenge-public, submission/board/1-18-m10-kh-a1.ec, commit 6e648ca0edb60bd7dc4d738df88bfdc34b373a27.\r\n\r\nOwn find (kshitij-hash lane): Mestre ten-root construction, roots [0,1,6,35,45,65,76,90,93,111]. The source supplies 18 rational points and states certified rank 18. This is a Layr-Labs result.",
  "created_at": "2026-11-01 00:32:27",
  "updated_at": "2026-11-01 00:32:27"
}