{
  "id": 3027,
  "curve_key": "4464786227421584554259421364260193:-214424772764799860495045726326367296863524526731665",
  "ainvs": [
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    "0",
    "0",
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  "rank_lower_bound": 8,
  "torsion": [
    4,
    2
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  "naive_height": 232.44458821376588,
  "faltings_height": 17.39570637336948,
  "conductor": "5449964496197021254957004621574",
  "bad_primes": [
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    "3",
    "7",
    "13",
    "23",
    "29",
    "107",
    "383",
    "397",
    "673",
    "1021",
    "10069",
    "132945913"
  ],
  "discriminant": "24898423962512792046660013666778186155648619498735623325680799704388820651104353560399195767046144",
  "regulator": "175563444.996460777248602114607375887896425325511446068",
  "points": [
    [
      "724518345330180",
      "425634897071619210739518"
    ],
    [
      "2466343285334784",
      "183763137126139307726562"
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    [
      "-243339027083388",
      "-520381520139590912837826"
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    [
      "-3049210233396",
      "-498458069246280103970346"
    ],
    [
      "1400661774217218",
      "347333018067921149283186"
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    [
      "4923987111172809716/25",
      "10913426769918985868266471174/125"
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    [
      "-8315627616507174",
      "-668313957994846830984108"
    ],
    [
      "189304695352472445/16",
      "57382453476457944122564163/64"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Dujella - Peral (2017). Source: https://dujella.github.io/tors/z2z4old678.html (curve entry 15). Published independent points; exact point coordinates checked.",
  "created_at": "2026-09-26 20:33:55",
  "updated_at": "2026-09-26 20:33:55"
}