{
  "id": 3057,
  "curve_key": "1115539274522223112571066676828001:-33726877099465435783169215257969936942201105199249",
  "ainvs": [
    "1",
    "0",
    "0",
    "-23240401552546314845230555767250",
    "39035737383640548738264240132679708432408668932"
  ],
  "rank_lower_bound": 8,
  "torsion": [
    4,
    2
  ],
  "naive_height": 228.28393803321774,
  "faltings_height": 16.994805229139835,
  "conductor": "27945024266811292803708345030",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "19",
    "23",
    "41",
    "47",
    "83",
    "103",
    "107",
    "149",
    "157",
    "353",
    "389",
    "4889"
  ],
  "discriminant": "145084448935738519618593364955279020010298843831556341576434203817845451452471505554180669440000",
  "regulator": "2603435.11138096018842283363770839856804105194145195670",
  "points": [
    [
      "2040837862129604",
      "10294405331164056123998"
    ],
    [
      "1546125919559684",
      "82457093881535497643678"
    ],
    [
      "1127689628153444",
      "119422955102773909527518"
    ],
    [
      "1146935474467964",
      "117852641604632336320958"
    ],
    [
      "1559355735815744",
      "81162787604838366316418"
    ],
    [
      "-2633076962819836",
      "-286311249696516774300322"
    ],
    [
      "-2051742007175356",
      "-279431456561050060030882"
    ],
    [
      "3795308235097924",
      "74163692520455985675358"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Dujella - Peral (2012). Source: https://dujella.github.io/tors/z2z4old678.html (curve entry 7). Published independent points; exact point coordinates checked.",
  "created_at": "2026-09-26 20:35:17",
  "updated_at": "2026-09-26 20:35:17"
}