{
  "id": 3221,
  "curve_key": "-664422678569932111606729722401696879:-1996339899774776090566537465356358135127540506520874169",
  "ainvs": [
    "1",
    "0",
    "0",
    "13842139136873585658473535883368685",
    "2310578587702287143012929957420435535344485058013217"
  ],
  "rank_lower_bound": 15,
  "torsion": [
    2
  ],
  "naive_height": 250.06182095107658,
  "faltings_height": 18.904533782685238,
  "conductor": "6098008034408866436674675605910737655832159836307310",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "17",
    "23",
    "29",
    "31",
    "53",
    "67",
    "97",
    "131",
    "191",
    "223",
    "227",
    "313",
    "433",
    "2609",
    "3881",
    "8689"
  ],
  "discriminant": "-2476092226426894410695170869028111842135118199889900449120195019566062513826231788992165893422560000000000",
  "regulator": "6180116111881592.6507773320954856914800152486886638985640124714279697",
  "points": [
    [
      "122297614621067374",
      "76371517653697877352456313"
    ],
    [
      "-83732000697566876",
      "-23759198445595187766047687"
    ],
    [
      "25441067662683214",
      "51761028418949259675488953"
    ],
    [
      "73953816612765874",
      "61145100990660665734144813"
    ],
    [
      "34832022390612950254",
      "205575107269815996538774839193"
    ],
    [
      "40055275609337374",
      "54122961609888925621386313"
    ],
    [
      "41494881996289582",
      "54372819039684046901077753"
    ],
    [
      "-41972894336652626",
      "-40689547714679739179783687"
    ],
    [
      "3136354086645978414",
      "5558520651891938736366377433"
    ],
    [
      "-82923898375968626",
      "-24341709003753460397711687"
    ],
    [
      "-82532657984748626",
      "-24616403601647205397451687"
    ],
    [
      "-5623744936084986",
      "-47249931938065315398104247"
    ],
    [
      "62724008442088794946/529",
      "912025929019355834260539572171/12167"
    ],
    [
      "665259823510317866494/121",
      "17162848762624869194438013238523/1331"
    ],
    [
      "6421783216109867310766/10609",
      "526871501011269788489694652535551/1092727"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Dujella (2009). Source: https://dujella.github.io/tors/z2old141516171819.html (curve entry 50). Published independent points; exact point coordinates checked.",
  "created_at": "2026-09-26 20:43:17",
  "updated_at": "2026-09-26 20:43:17"
}