{
  "id": 604,
  "curve_key": "3385625830586674935693342547450091761992721:-6004779753931464832417911784745337554518895633088548494090095481",
  "ainvs": [
    "1",
    "0",
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  ],
  "rank_lower_bound": 23,
  "torsion": [],
  "naive_height": 293.784338035522,
  "faltings_height": 22.405766680832034,
  "conductor": "672916189200493189932374678182269172081492583885865619151065602052989614759908631144798052376110",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "13",
    "17",
    "23",
    "31",
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    "67",
    "439",
    "11718406088935243351936391947315867132645945128746069272589709901238939675400392501"
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  "discriminant": "1591567379854769932366973346865870374064343213115496228989012319224530864151866247958524555838312057089713009545950720000000",
  "regulator": "5281924458658906845065944.56491797783361990269348272498513343047350030545076853063883",
  "points": [
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      "519928877393321113130",
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      "-756853689930854975441321636815"
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      "6816283346024501311130/841",
      "61597719848021324565264865670188465/24389"
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      "1961067750510520510543030965185"
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      "-564067029396321907118530/2209",
      "299311447030323090539320751582398255/103823"
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      "-30433954740081577090",
      "-3011380499191799406294854285215"
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      "-101597155158291980353474565631535"
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      "2324369153721557050430",
      "111359120715353723932457949921185"
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      "-1767209835653227275163/16",
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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 = -215/89. 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 15:46:08",
  "updated_at": "2026-09-06 15:46:08"
}