{
  "id": 3193,
  "curve_key": "363024812750091454148025957649:-333823126849823149236945044295880037345656057",
  "ainvs": [
    "1",
    "0",
    "0",
    "-7563016932293571961417207451",
    "386369359779887273958016110137382888086481"
  ],
  "rank_lower_bound": 14,
  "torsion": [
    2
  ],
  "naive_height": 205.03837039626032,
  "faltings_height": 15.117416419159959,
  "conductor": "37047639080308908544920171799389911308078271310",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "29",
    "109",
    "113",
    "157",
    "173",
    "541",
    "827",
    "2083",
    "4231",
    "5171",
    "14177",
    "1708781"
  ],
  "discriminant": "-36803196583049775813483789459555313264990161929395173729711391879394432512725511065600",
  "regulator": "7284355431267436.97411033272925033869205628705858532887334812345943",
  "points": [
    [
      "66767376437326",
      "423140231789716881937"
    ],
    [
      "-9144873957554",
      "-674364453464665338863"
    ],
    [
      "12529961180047156/81",
      "1245305883208100001392323/729"
    ],
    [
      "-104289251220674",
      "-202076618783126154863"
    ],
    [
      "-101540199122414",
      "-327716768598151710983"
    ],
    [
      "-47091677018864",
      "-798807075201939840953"
    ],
    [
      "17546944193347186/289",
      "1909121817951638820440069/4913"
    ],
    [
      "6496704677251840/49",
      "449100315418851513581233/343"
    ],
    [
      "-105826098639194",
      "-39625584501587663903"
    ],
    [
      "256380787837048954/3721",
      "99553155072107759480970913/226981"
    ],
    [
      "41025161952201947614/2518569",
      "2067236229026733299084170388891/3996969003"
    ],
    [
      "255111346692991103824/16834609",
      "36237644966030676192257928030959/69072400727"
    ],
    [
      "39628940233241058646834/267878689",
      "6939397994014654564678230871020311/4384370502863"
    ],
    [
      "17246400470544478/67081",
      "10772216401655188406489710603/17373979"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Dujella (2009). Source: https://dujella.github.io/tors/z2old141516171819.html (curve entry 72). Published independent points; exact point coordinates checked.",
  "created_at": "2026-09-26 20:42:01",
  "updated_at": "2026-09-26 20:42:01"
}