{
  "id": 609,
  "curve_key": "76929167432608566610067421947392649235561936:-660566407635079848196434505773749714187718185374436683195604954816",
  "ainvs": [
    "0",
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    "764544453281342416894021418719617724754303455294486901846764994"
  ],
  "rank_lower_bound": 23,
  "torsion": [],
  "naive_height": 303.1543770022804,
  "faltings_height": 23.161237249008977,
  "conductor": "4118482257964122577897131179164327389821105780521383211377216820453903957341851856458623320",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "17",
    "29",
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    "61",
    "71",
    "83",
    "109",
    "3721035415760065191439636281120916611382462235483020039054732413643738793"
  ],
  "discriminant": "10952708829780421468861171587400899127893190865905526538295036012931357472584527738913978077083210441001377621186740755812000000",
  "regulator": "413197019706297631631648.459752336395905432378189929638606677701963822695691275002915",
  "points": [
    [
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      "-29003411221458379583664270734250"
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      "5643992108564476158313",
      "414133245477585792163297989155550"
    ],
    [
      "10084157165821124866507/9",
      "523171398516415218530235179744840/27"
    ],
    [
      "637935018080473072963",
      "1321543544595603340445213379600"
    ],
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      "-157737307405731826263296453097450"
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      "153656056077434143418",
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      "10200812511437743276966/9",
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  "submitter": "Bhavik Mehta",
  "history": [],
  "commentary": "Found by specializing Noam D. Elkies's rank-17 elliptic K3 fibration (arXiv:2608.25406) at t = -829/254. The 6 points beyond the seventeen generic sections come from the surface's rational quadratic sections: writing x_tau = a/c^2 and y_tau = b/c^3 for a trace of height 10, the slope of the bisection is forced to be kappa/c with kappa = -b*a^(-1) mod c^2 of degree 5, so each section's point on this fibre is obtained by one polynomial evaluation and one square test rather than by any search. Claimed lower bound: rank >= 23.",
  "created_at": "2026-09-06 15:47:07",
  "updated_at": "2026-09-06 15:47:07"
}