{
  "id": 620,
  "curve_key": "19965030363531231520435863457171597016469929474658689030446081:-88639353870241121011586819805427655948909901276619443524642588606153582242746512505097259521",
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  "rank_lower_bound": 28,
  "torsion": [],
  "naive_height": 423.4472635229844,
  "faltings_height": 33.13323381559401,
  "conductor": "34363954940293776614841021425585547642251609013785254548912325067825448439331718049552978507578606223080831625486859605329767365039492740373364087010",
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      "-10056851915288516510045049935024393577854013820/27"
    ],
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      "649816207883349504542726921238231840/1274641",
      "-218448655233879477543967917629613270243269529385494240/1439069689"
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  ],
  "submitter": "Mundoamundo",
  "history": [
    {
      "kind": "primes_recorded",
      "user": "Daniel Błażewicz",
      "at": "2026-09-11 19:43:41"
    }
  ],
  "commentary": "Fiber t = 45532/1617 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 22:23:00",
  "updated_at": "2026-09-11 19:43:41"
}