{
  "id": 6378,
  "curve_key": "103899951491412076624:-1059593118332958705521939222168",
  "ainvs": [
    "0",
    "-1",
    "1",
    "-2164582322737751596",
    "1226380924718007424155569076"
  ],
  "rank_lower_bound": 19,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 138.2708755472531,
  "faltings_height": 9.271112638683231,
  "conductor": "6155359341987891556276460466971039662842592963042515",
  "bad_primes": [
    "3",
    "5",
    "7",
    "1979",
    "755551",
    "14894974781",
    "771979522310093",
    "3409643562192599"
  ],
  "discriminant": "-646312730908728613409028349031959164598472261119464075",
  "regulator": "24121063400811601.74515872400313217251772307685224444906812877935051725959936",
  "points": [
    [
      "779978653",
      "3544849536292"
    ],
    [
      "855753589",
      "-844003492445"
    ],
    [
      "394844704",
      "20815001115940"
    ],
    [
      "879342370",
      "1708013362912"
    ],
    [
      "-40110117",
      "36237246652022"
    ],
    [
      "57319831",
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    ],
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      "1620028720",
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    ],
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      "1221279194",
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    [
      "880372926",
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    ],
    [
      "2512751733",
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    ],
    [
      "-1120325456",
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    ],
    [
      "-1347661334",
      "41181237739519"
    ],
    [
      "-1539997499",
      "30126169352044"
    ],
    [
      "1079014970",
      "-12125696652608"
    ],
    [
      "7088118508",
      "584808286582852"
    ],
    [
      "8777658082/9",
      "-177000962359931/27"
    ],
    [
      "238017219",
      "26919458727425"
    ],
    [
      "-1692149902",
      "-6627611784353"
    ],
    [
      "-1417423121",
      "38036584233109"
    ]
  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "From the Layr-Labs elliptic-rank-challenge-public repository (https://github.com/Layr-Labs/elliptic-rank-challenge-public, file submission/board/1-19-m10-203427.ec), where it is recorded as a find of that challenge; not our discovery. Posted by apkorte with Claude (Anthropic), which moved the points to the minimal model and checked their independence.",
  "created_at": "2026-11-01 20:51:45",
  "updated_at": "2026-11-01 20:51:45"
}