{
  "id": 2859,
  "curve_key": "170969540329344461298986102881:-70377089442293768311237273417539133220232721",
  "ainvs": [
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    "0",
    "-3561865423528009610395543810",
    "81454964632284157241813402084313871228100"
  ],
  "rank_lower_bound": 5,
  "torsion": [
    8
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  "naive_height": 201.93384877423938,
  "faltings_height": 14.659095611206848,
  "conductor": "468965404423650544410",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "19",
    "43",
    "67",
    "97",
    "449",
    "1409",
    "4649"
  ],
  "discriminant": "25812930481056227322154830716230493339922335758593354520224586250215976985600000000",
  "regulator": "71311.1820333515500019384401531710125543107352671",
  "points": [
    [
      "5949581008982",
      "245914531223693387432"
    ],
    [
      "-1195249703128",
      "-292763685098693066518"
    ],
    [
      "71998581355220",
      "445232088662833121390"
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    [
      "982331112925220",
      "30732830735127701753390"
    ],
    [
      "56005666625120",
      "240082528969829449490"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "MacLeod (2012). Source: https://dujella.github.io/tors/z8old5.html (curve entry 4). Published independent points; exact point coordinates checked.",
  "created_at": "2026-09-26 20:25:41",
  "updated_at": "2026-09-26 20:25:41"
}