{
  "id": 3553,
  "curve_key": "96534874522545779328788876186911049571417774721:-26055561797615687278027176338300410231213808062187236523755456285548481",
  "ainvs": [
    "1",
    "0",
    "0",
    "-2011143219219703736016434920560646866071203640",
    "30156900228721860275494249462949799088593535739436291848589235137600"
  ],
  "rank_lower_bound": 19,
  "torsion": [
    2
  ],
  "naive_height": 324.5587005654178,
  "faltings_height": 25.03408043741588,
  "conductor": "2155758992663991692041802618212395866297853180989658043025602632708992617830",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "17",
    "43",
    "59",
    "61",
    "67",
    "307",
    "461",
    "659",
    "769",
    "773",
    "1153",
    "1487",
    "1609",
    "8521",
    "84827",
    "176597",
    "261059",
    "410741",
    "2959403",
    "5976301"
  ],
  "discriminant": "127728273940991751526831777509461870520562200054193578351524251213119481632970794325550812349344353824763607619550311975640307246694400000",
  "regulator": "5296103457971436711381.191160296996372341965129436930874522854970906654917159",
  "points": [
    [
      "-37963651047014588678720",
      "7196704294278910878670205728599160"
    ],
    [
      "-15512066175475223864720",
      "7590870073051438655443239488265160"
    ],
    [
      "-5501897083210849781670",
      "6407453161811704595908706469033060"
    ],
    [
      "39039345471925779015280",
      "3337948452717648121050995021999560"
    ],
    [
      "169761241712095724812912",
      "67683612829879392119753446349449672"
    ],
    [
      "-54280914649362211771279857440/8427409",
      "160133922521183842240085239442291288361390200/24464768327"
    ],
    [
      "-37057592621652218812903280/729",
      "20020031028806131792500736359183631480/19683"
    ],
    [
      "-3386571036006812477951120/81",
      "4676822880110955868899455649788360840/729"
    ],
    [
      "594005051740658826162160/361",
      "35542682133992686800945376812255066520/6859"
    ],
    [
      "620921688510517710801688/9",
      "400283767348492203269076525495046744/27"
    ],
    [
      "5114572894346221122475120/289",
      "1611537693646591644614233015041636680/4913"
    ],
    [
      "24276032166241420312732720/17689",
      "12314752925605815948307160835789037668520/2352637"
    ],
    [
      "33528660119676186977729700/961",
      "46716401925549958703693655220114121640/29791"
    ],
    [
      "43691876631631499884774882/3481",
      "539148426535818155457600199653883552574/205379"
    ],
    [
      "66673483685570273436465520/8649",
      "3126816567599850036925471670810347903720/804357"
    ],
    [
      "1956306335951545190242446880/32761",
      "65762306463577993547287148295207360264760/5929741"
    ],
    [
      "4779494555210410710517341520/69169",
      "270503476014622137249377179167311735004920/18191447"
    ],
    [
      "33315290198269273781580294616/265225",
      "5729430071838979605911176609448033356941344/136590875"
    ],
    [
      "1061692109765059301501994831600/13830961",
      "931697938901122072439975935722409524038576760/51437343959"
    ]
  ],
  "submitter": "Matej Jurasić",
  "history": [],
  "commentary": "Rank exactly 19, torsion Z/2Z. Specialization at T = 51349/6454 of the rank-9 fibration of X400 (equations as in curve#802).",
  "created_at": "2026-09-28 10:48:46",
  "updated_at": "2026-09-28 10:48:46"
}