{
  "id": 435,
  "curve_key": "23577975531108894405024044744056426561:-115890269442310189844528499021172087314294003158605561441",
  "ainvs": [
    "1",
    "0",
    "0",
    "-491207823564768633438000932167842220",
    "134132256298970127093936962644107344568006870419584400"
  ],
  "rank_lower_bound": 20,
  "torsion": [],
  "naive_height": 258.18447762401064,
  "faltings_height": 19.388712963689805,
  "conductor": "123075360516683336654553303844383299197909575873281085669191642645264530494551661964770",
  "bad_primes": [
    "2",
    "3",
    "5",
    "13",
    "37",
    "79",
    "4007",
    "17669",
    "8512039",
    "1766124707838611",
    "101435835322593306728071336404869210405812124818463"
  ],
  "discriminant": "-186958601393353252327110498841398254188347817102394513204661439461977075991984262361321535370901510400000000",
  "regulator": "3705880620238679320250.29168292770768152586822708798026324741640090924409721055",
  "points": [
    [
      "40838553511767320",
      "-337846339852693382537605420"
    ],
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      "366425412797439590",
      "-57795167443891501590647920"
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      "49212210585677384124657812"
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      "-35355377301999160",
      "-389172069788933719229005420"
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    [
      "1103477090798054840",
      "967345571278400532217090580"
    ],
    [
      "1853400678503207090",
      "-2364388512209569933886249170"
    ],
    [
      "163561244489712604370/289",
      "-950248241338883047220401741280/4913"
    ],
    [
      "785031764540957840",
      "-481989483160081856190685420"
    ],
    [
      "325041624449940872",
      "-93864710367607361756902684"
    ],
    [
      "37873571236452314390/121",
      "139897997056148676557614114480/1331"
    ],
    [
      "4933239588345764765/16",
      "-7008159686299436628002309005/64"
    ],
    [
      "1708850342053651640",
      "-2069991361572707163592189420"
    ],
    [
      "112051284482741432",
      "-283722835834304811640221388"
    ],
    [
      "-786318334054936660",
      "184932642990043922970432080"
    ],
    [
      "42714225031433289140/121",
      "91459006904937138737703223480/1331"
    ]
  ],
  "submitter": "Bhavik Mehta",
  "history": [],
  "commentary": "Found by specializing Noam D. Elkies's rank-17 elliptic K3 fibration (arXiv:2608.25406) at t = 40/3. 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 04:29:51",
  "updated_at": "2026-08-30 04:29:51"
}