{
  "id": 580,
  "curve_key": "3763287543693177274806248172899188008787771588201582339225201:-7635549028868048012734671846815375853469249879931189957727522093030959243443725532833053449",
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  "rank_lower_bound": 28,
  "torsion": [],
  "naive_height": 418.5309464300556,
  "faltings_height": 32.810106008888425,
  "conductor": "36510756000952665280030063659319619364796897551455221288210622984978144848004074984277874902165016599942052931713561475909811125772658104689009595610",
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      "40112993315597448580088638173346855000594676251409628817/467107946479"
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      "3565993695928635552503818220642087356594/11028990361",
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    ],
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      "-38454729717665846894383787396",
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      "-173535038980929046861581753734917222613756888850581/3869893"
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  ],
  "submitter": "Mundoamundo",
  "history": [
    {
      "kind": "primes_recorded",
      "user": "TristanPhillips",
      "at": "2026-09-05 11:25:17"
    }
  ],
  "commentary": "Fiber t = -19733/38399 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 iterated 'bootstrap' 2-covering point search (fake 2-descent over cosets of the growing known lattice, minimal reduced quartic models, ratpoints). 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 18:49:50",
  "updated_at": "2026-09-05 11:25:17"
}