{
  "id": 2821,
  "curve_key": "740703606815790766639104546660001:-24257544188146276089929569085326214742179769990001",
  "ainvs": [
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    "28075861328873003447771017200972297203151562500"
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  "rank_lower_bound": 5,
  "torsion": [
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  "naive_height": 227.4256242665161,
  "faltings_height": 16.950245345385316,
  "conductor": "552116366801381712611190",
  "bad_primes": [
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    "3",
    "5",
    "7",
    "13",
    "19",
    "79",
    "97",
    "991",
    "4451",
    "314908439"
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  "discriminant": "-105351542462786455799105153105482610330131986512360815752533009850830722462115666323046400000000",
  "regulator": "650206.438105453436285000059984220164526811117872",
  "points": [
    [
      "-3933616698398660",
      "-167064625300798315877150"
    ],
    [
      "-304174496034500",
      "-180946218395393828126750"
    ],
    [
      "30125238846195629500/1089",
      "163781914453907721439422841250/35937"
    ],
    [
      "4704373642915683100/841",
      "8334771827186805028417366250/24389"
    ],
    [
      "3873097779952529057020/3129361",
      "577240587069060000283078461520850/5535839609"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Dujella - Peral (2012). Source: https://dujella.github.io/tors/z8old5.html (curve entry 7). Published independent points; exact point coordinates checked.",
  "created_at": "2026-09-26 20:23:55",
  "updated_at": "2026-09-26 20:23:55"
}