{
  "id": 608,
  "curve_key": "46712847219698315195495057527402589468335696:-167284079409567486723308168313694408453208660634339337693951735744",
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  "rank_lower_bound": 23,
  "torsion": [],
  "naive_height": 301.65777940096683,
  "faltings_height": 23.18713376797454,
  "conductor": "168979098173352083998670678858011914126690850746126480609555833436313402102894742081580070200120",
  "bad_primes": [
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  "discriminant": "42793795150908683102506355460476642413127991275720487254267323117993866206292557273288532148104447561517620299588169176244000000",
  "regulator": "3384205942643454163485015.19850576365745472436349339841317486238899999002293113052124",
  "points": [
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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 = -67/142. 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 15:46:55",
  "updated_at": "2026-09-06 15:46:55"
}