{
  "id": 433,
  "curve_key": "65532015972665727970154403739528656:-17387261482218646477924417935700525139539379468856000",
  "ainvs": [
    "0",
    "0",
    "0",
    "-1365250332763869332711550077906847",
    "20124145234049359349449557795949681874466874385250"
  ],
  "rank_lower_bound": 22,
  "torsion": [],
  "naive_height": 240.57515516415722,
  "faltings_height": 17.969945520680113,
  "conductor": "8767703080908304246350044139590743239251700950560208898265331557899477239062701912",
  "bad_primes": [
    "2",
    "3",
    "7",
    "11",
    "13",
    "127",
    "173",
    "467",
    "79490093273809",
    "542758304000375563517",
    "39258620240424693354641956745935193"
  ],
  "discriminant": "-12090981377961386591784512998993507250890722176967802591484974773130916656682489069003465618447324928",
  "regulator": "35622604278554946591845.62375391998939925032321571319415160914222824511689920758636",
  "points": [
    [
      "-21318875892564579",
      "-6288118673751306392182182"
    ],
    [
      "-34850092549290501",
      "-5037539017053598096490064"
    ],
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    ],
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    ],
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      "-20622194291944254695782352256"
    ],
    [
      "-169341729552119439/4",
      "11441078481091034428205553/8"
    ],
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      "50402243117358573",
      "-8908065134347878285118794"
    ],
    [
      "162128482797677925",
      "63721502749831694280328530"
    ],
    [
      "3832411807696367217/4",
      "-7497043568525118274478788977/8"
    ],
    [
      "105157259270017626",
      "32239607726655472612867398"
    ],
    [
      "-10824292539002271",
      "5799463996365775437527826"
    ],
    [
      "29435847740396769",
      "-2332830417830666708708754"
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    [
      "23421592852483497",
      "-998105548607675724173958"
    ],
    [
      "-32834128279281",
      "4490987864959205492979096"
    ],
    [
      "-228290194493781",
      "-4520598035700883303263096"
    ],
    [
      "-8893453237285847/144",
      "-7768020799173978087621014699/1728"
    ],
    [
      "1207041375047809/4",
      "35518733583190143267304169/8"
    ],
    [
      "348063743694325",
      "-4432718495404680600571010"
    ]
  ],
  "submitter": "Bhavik Mehta",
  "history": [
    {
      "kind": "rank_improved",
      "user": "Jason Ma",
      "old_rank": 21,
      "new_rank": 22,
      "at": "2026-09-03 16:27:57"
    }
  ],
  "commentary": "Found by specializing Noam D. Elkies's rank-17 elliptic K3 fibration (arXiv:2608.25406) at t = -11/10. The 4 points beyond the seventeen generic sections came from searching the 1311 norm-4 quartic covers of the Mordell-Weil lattice; the claimed lower bound is rank >= 21.",
  "created_at": "2026-08-30 04:29:50",
  "updated_at": "2026-09-03 16:27:57"
}