{
  "id": 612,
  "curve_key": "200475952041689051950227421959188810094631036801:-88717119785079116590220222030841106166023641152916422293821961790395201",
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  "rank_lower_bound": 24,
  "torsion": [],
  "naive_height": 326.7510704530308,
  "faltings_height": 25.10108387820004,
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  "discriminant": "107941509298485682587711104636524800379500922558245365430167053358366222380718250222801737930831670091202220934299800199778516881408000000",
  "regulator": "123910445565995663220169923.36328632061038312084919721795546458613328107479163582293607",
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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 = -3422/429. The 7 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 >= 24.",
  "created_at": "2026-09-06 15:47:42",
  "updated_at": "2026-09-06 15:47:42"
}