{
  "id": 581,
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  "rank_lower_bound": 28,
  "torsion": [],
  "naive_height": 415.6804640616297,
  "faltings_height": 32.439168808784565,
  "conductor": "466327614591319361199238779339055872306377700125464700689888547207305294084079816938021468859497088226788021318593951936213767879940235870192830050",
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  ],
  "submitter": "Mundoamundo",
  "history": [
    {
      "kind": "primes_recorded",
      "user": "Daniel Błażewicz",
      "at": "2026-09-11 20:16:54"
    }
  ],
  "commentary": "Fiber t = -22059/24335 of a rank-17 elliptic fibration of Elkies' K3 surface (arXiv:2608.25406): the 2-neighbour fibration that also carries wgxli's #356, #385 and #351. Found by a Mestre-Nagao sieve over t = a/b re-scored at 2^20, followed by an exhaustive GPU sweep of all 131071 cosets of the section lattice modulo 2 with a 2-covering point search on each (fake 2-descent, minimal reduced quartic models). A cheaper 96-coset probe of this fiber had found nothing. Basis LLL-reduced with respect to the canonical height. The 28 points are certified independent by the F2-rank of their images under the 2-descent map at the good primes.",
  "created_at": "2026-09-04 18:51:59",
  "updated_at": "2026-09-11 20:16:53"
}