{
  "id": 603,
  "curve_key": "2292022927598800220281072229223797631815281:-3503460915625083766943188606039864396568102385873490475564465929",
  "ainvs": [
    "1",
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  ],
  "rank_lower_bound": 23,
  "torsion": [],
  "naive_height": 292.6332243431653,
  "faltings_height": 22.2491477275304,
  "conductor": "16854864852052069315413395831973557760017593822284352366748443540111622952880842175074981539057190",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "17",
    "37",
    "127",
    "255586897",
    "27490142467359115890200291762103480608547729694090727479231177319757972234785423"
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  "discriminant": "-135067107355235827701563800268694131505662911123744756908069759287770973858669928043476649844893154734718961519958224000000",
  "regulator": "12815207646561990534272173.4343510057661636705941743969084899338763872316991961313001",
  "points": [
    [
      "-162526653026313769466",
      "2742723015400181888064300656983"
    ],
    [
      "-221723272868789275766",
      "-1934461031511398477835560411417"
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      "12718711336175444953756/9",
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      "2557716623625385910701182971823"
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      "28216347098937058203381043359583"
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      "131856941322002028842866/1849",
      "-79997681198337701683568094821821619/79507"
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      "-547308673751701909846397001767"
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      "-2939745244760404707916535499617"
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      "94939966430229646848715174928983"
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      "3102426401727248288465812/37249",
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      "919950260704822908106/9",
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      "-150559441996951175006/25",
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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 = -831/416. 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 15:45:56",
  "updated_at": "2026-09-06 15:45:56"
}