{
  "id": 355,
  "curve_key": "12137054955226359390718109311139379216:-42611969255495133635514475601447252577710484968217315264",
  "ainvs": [
    "0",
    "0",
    "0",
    "-252855311567215820639960610648737067",
    "49319408860526775041104717131304690483461209453955226"
  ],
  "rank_lower_bound": 20,
  "torsion": [],
  "naive_height": 256.1834604078568,
  "faltings_height": 19.202490461896485,
  "conductor": "2160288978585670445440893546206560240112122473979420022281459005989256431760",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "17",
    "19",
    "31",
    "37",
    "313",
    "489539",
    "1439239",
    "7617780311",
    "4815998457419707882431488757218133251231"
  ],
  "discriminant": "-16142003783445781808920938206778271203651911584288646693594818011146385545148748364251510614775307220480000",
  "regulator": "60699467860927856405.7857195187468274002341485131977537494878518443962250770842",
  "points": [
    [
      "-2019638822022837268554628060527069249/19366699711524400225",
      "23271220611078251714252322519158890577410146068310651374/85228221921363254612537284625"
    ],
    [
      "237292716256906007",
      "51769912522766509079198190"
    ],
    [
      "75719202682312571307917/57121",
      "-19515390232494012363627781135587840/13651919"
    ],
    [
      "6241929306731715293268837/7946761",
      "12972095229065046901674305078832534400/22401919259"
    ],
    [
      "41515401984098717524106/143641",
      "1063660727220632857541293193615490/54439939"
    ],
    [
      "2582123612099476443072143/66049",
      "4148869687928413151001662993884523730/16974593"
    ],
    [
      "66070813229272491636167/160801",
      "7842720084745284093661417461567150/64481201"
    ],
    [
      "159561026024221941854705/440896",
      "-21131026401576460665576265096310199/292754944"
    ],
    [
      "694236840396406578437/1681",
      "8534154877690388294740269837960/68921"
    ],
    [
      "17832388216180302488263277/50537881",
      "-22809133813732305932795550052228223400/359273796029"
    ],
    [
      "510503669931442179383/1849",
      "1870633910470598662424382494550/79507"
    ],
    [
      "4767314810716245034493/18769",
      "98963993966545053367132154883840/2571353"
    ],
    [
      "16102269042459691313/64",
      "20658837558856555451679881175/512"
    ],
    [
      "512190929896341794825/3364",
      "23372884323810767836511458023987/195112"
    ],
    [
      "13181425042723441447713818/51509329",
      "-13688697532112984552723148714721654050/369682454233"
    ],
    [
      "2351806560534061093/9",
      "890880483732373169998066720/27"
    ],
    [
      "21883919004732365062/81",
      "19637444545642881553756820660/729"
    ],
    [
      "-20373664434769795",
      "-233372109091778885949247296"
    ],
    [
      "71086902629927039285/289",
      "220028355418023356251758269832/4913"
    ],
    [
      "-88338389965092882328164697/220908769",
      "-965596571633535865831787784518349081810/3283367033647"
    ]
  ],
  "submitter": "7fff-zip",
  "commentary": "Found in the Mestre-family search; the listed 20 rational points are independently certified (roots=[0, 239, 3790, 4812, 4879, 5762], T=13522/7).",
  "created_at": "2026-08-25 14:10:27",
  "updated_at": "2026-08-25 14:10:27"
}