{
  "id": 447,
  "curve_key": "394732951977013484503724450247393121:-250061829866545012849919395203527392233265064467860625",
  "ainvs": [
    "1",
    "0",
    "0",
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    "289423414197390060483587925043989774858424061454596"
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  "rank_lower_bound": 20,
  "torsion": [],
  "naive_height": 245.9070958988927,
  "faltings_height": 18.34894229532944,
  "conductor": "45489840601228627635532811975031132007507587327025647851680639923793222795626",
  "bad_primes": [
    "2",
    "3",
    "7",
    "11",
    "13",
    "17",
    "19",
    "31",
    "59",
    "45856001",
    "22512999527441173827379",
    "1774129343087441674531448761910137421"
  ],
  "discriminant": "-593725561778098105732039277778467901025058153749125977677261165119338828075776800959848024867639001088",
  "regulator": "99849115668872990442.0823918198327769762141903496892247407867405684592549042677",
  "points": [
    [
      "-3050623824859516",
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      "36923320941468551062354334"
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      "48963249048566948",
      "2038029829301716521456638"
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      "93994325290766996",
      "18624848060331895229433038"
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    [
      "127970250866838020",
      "-36506670199943912043237346"
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    [
      "34238219544710276",
      "-6928046696869381715646562"
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    [
      "929069325871188116",
      "891399865794604667962183838"
    ],
    [
      "82576123193497028",
      "13168961426818025420257118"
    ],
    [
      "136970807713942388",
      "-41626187335393524094640866"
    ],
    [
      "40246811804290550",
      "4862265587396403209484914"
    ],
    [
      "35120114870189444",
      "-6627779821615801625303074"
    ],
    [
      "153500403738398290148/121",
      "1897067452977640428877137904954/1331"
    ],
    [
      "-101874965787498172",
      "8360172975611561262077918"
    ]
  ],
  "submitter": "Bhavik Mehta",
  "history": [],
  "commentary": "Found by specializing Noam D. Elkies's rank-17 elliptic K3 fibration (arXiv:2608.25406) at t = 12/5. 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 15:55:00",
  "updated_at": "2026-08-30 15:55:00"
}