{
  "id": 6418,
  "curve_key": "50282427375662946376566801:-357588896946261794067077812862054392185",
  "ainvs": [
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    "-1",
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    "413876038132509334479477194584200165"
  ],
  "rank_lower_bound": 21,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 177.54489468358997,
  "faltings_height": 12.60917877981199,
  "conductor": "1685454917805383803661722878638558094370688613417272529519797690854",
  "bad_primes": [
    "2",
    "31",
    "22067313251",
    "1231901520116619155808160457660558454281984448893045167"
  ],
  "discriminant": "-428024647286512827707501848476019105181625114754543193416611663187755008",
  "regulator": "90675234578361487613.777284126280685798903038254748702765823809036231623463489358",
  "points": [
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    ],
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    ],
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    [
      "5853988706029/9",
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    [
      "17404057026849/25",
      "18540566137872292383/125"
    ],
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    ],
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      "854640678451",
      "-377936129545337069"
    ],
    [
      "2994078089663/4",
      "1773501702287171911/8"
    ],
    [
      "48118068420313/81",
      "25422326819799931891/729"
    ],
    [
      "31230273433321",
      "-174434875974044015093"
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    [
      "23011399708601/25",
      "59882413580778741559/125"
    ],
    [
      "85916533488301/9",
      "791970452952867528205/27"
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  ],
  "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/1-21-m10-131401.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": "2026-11-02 14:15:54",
  "updated_at": "2026-11-02 14:15:54"
}