{
  "id": 618,
  "curve_key": "334566581882007067303195221505509767658506103195133817183041:-192978219159630798160044831604537348558173765790512884994353998705912361367407849414885089",
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  "rank_lower_bound": 28,
  "torsion": [],
  "naive_height": 411.1805586281876,
  "faltings_height": 32.07746112126225,
  "conductor": "56028086190794798833781577518120957209584777040976670351674315922352499192998038665361259294688724967685308936002906025771359335350230",
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  "regulator": "2102485225710153985861312449786776.532123788966123819948767359974282353355738230881982570511165",
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      "-796999100692252113224801470064/9",
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      "19439042455032789771176458544",
      "9757416856465203009787031946630151024318028"
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      "169050407572792855456655389281024632/2686321",
      "-25649768579818112138571125301221385634628022909099940/4402880119"
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  ],
  "submitter": "Mundoamundo",
  "history": [],
  "commentary": "Fiber t = 17308/3257 of a rank-17 elliptic fibration of Elkies' K3 surface (arXiv:2608.25406). Found by a Mestre-Nagao sieve over t = a/b re-scored at 2^20, then an iterated 2-covering point search (fake 2-descent over 3000 cosets of the growing known lattice at level 0, 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": "2026-09-06 22:22:58",
  "updated_at": "2026-09-06 22:22:58"
}