{
  "id": 453,
  "curve_key": "45490670290100804995991575995616225:-9280458855924793313935845863467467279664445719731025",
  "ainvs": [
    "1",
    "0",
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    "10741271823987029219560000495736411788978103849892"
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  "rank_lower_bound": 20,
  "torsion": [],
  "naive_height": 239.4084459754976,
  "faltings_height": 17.883419034259827,
  "conductor": "13084625393869787313650703588177493604700881735528116368457036420717249161149679450",
  "bad_primes": [
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    "3",
    "5",
    "13",
    "43",
    "53",
    "79",
    "521",
    "189757",
    "18934786237",
    "60273449057849",
    "329976530182267181",
    "23279935841954019329597"
  ],
  "discriminant": "4636299657612563166681253329091306846826122114695724901421139822853342167905934630275298181345280000",
  "regulator": "1429616378236788333106.93030005646862421948609932056411497257016340596683829822",
  "points": [
    [
      "-883163106230566956/25",
      "-45893935868852866927232082/125"
    ],
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      "14651572852284942",
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      "1905212105488130066426694"
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      "2814750489621228",
      "2845341943746707529664110"
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      "-5530367090280111468/841",
      "99634587561235636514517988446/24389"
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      "1656723953981623044/25",
      "1932298619878530161696337918/125"
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    [
      "88252510990242243/4",
      "-6047695630033812578474373/8"
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      "21203413701522132",
      "-423149363319236182950426"
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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 = -13/9. The 3 points beyond the seventeen generic sections came from searching the 1311 norm-4 quartic covers of the Mordell-Weil lattice; the claimed lower bound is rank >= 20.",
  "created_at": "2026-08-30 15:55:04",
  "updated_at": "2026-08-30 15:55:04"
}