{
  "id": 411,
  "curve_key": "172391088998968150608536811694822081:-67722847277295401575974254002270504998437292077183521",
  "ainvs": [
    "1",
    "0",
    "0",
    "-3591481020811836471011183576975460",
    "78382925089462270043272708916456341534296382563600"
  ],
  "rank_lower_bound": 17,
  "torsion": [],
  "naive_height": 243.40522121326865,
  "faltings_height": 18.22686150814001,
  "conductor": "697471501244923640231031960671964527448437948533000993040265343878361788745830",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "17",
    "19",
    "23",
    "59",
    "787",
    "1042021",
    "176952289",
    "430133491",
    "121398733147020929713530078079397101059846241"
  ],
  "discriminant": "310678744110001122475227156478814685375156829579582715053262018879190161226305823287881164380160000000",
  "regulator": "155209831672360353574.757755050007669758851590780778648493274094317138972",
  "points": [
    [
      "24772322644184520",
      "2148389943036834842395740"
    ],
    [
      "9797686156275732930/1369",
      "368919106183525688476916031720/50653"
    ],
    [
      "3127017958357403112/961",
      "243359800761923022074485291812/29791"
    ],
    [
      "15592050629753408424/25",
      "-61293074017087733530093545492/125"
    ],
    [
      "1674203746121820045/16",
      "-1863996940466392330412181765/64"
    ],
    [
      "-112390364223206198280/1681",
      "305401375028158891231668012540/68921"
    ],
    [
      "5986328471188920",
      "-7556299814247835208928660"
    ],
    [
      "33550257927612894580086120/732189481",
      "62727270737791279502598168914350613460/19812315166379"
    ],
    [
      "41758887077046598429525320/815616481",
      "124816036374062328635704642716834162660/23293191080879"
    ],
    [
      "26107976801618252357845320/988410721",
      "-43353659186484769900596374963822880540/31074644657519"
    ],
    [
      "35172590531306519700988920/1270138321",
      "-18288836896342665268959226977127892940/45266459622119"
    ],
    [
      "131366953672641840165478920/1379305321",
      "1255040104245352540642133746995551187060/51226020316619"
    ],
    [
      "377944049651233472720128080/4725600049",
      "-5652061305995881889785586267169124402620/324851924168407"
    ],
    [
      "12183626297450520",
      "6036075631261013757163740"
    ],
    [
      "424311742787502149391780/9406489",
      "-82421836885359366200622052059940380/28849701763"
    ],
    [
      "153766157384885463753480/5841889",
      "-20393994738618935000024898895887780/14119845713"
    ],
    [
      "79475869502840520",
      "-17174088944055915491476260"
    ]
  ],
  "submitter": "Christopher R. Hill",
  "commentary": "Found with Rank Hunter v0.8.6.4; family=Campbell 1999 C6, generic rank >=13; parameter=5/2; local status: rigorous rank lower bound >= 17.",
  "created_at": "2026-08-28 22:41:11",
  "updated_at": "2026-08-28 22:41:11"
}