{
  "id": 2855,
  "curve_key": "328609734809499859942144474753:-205410571423100357593002444643944151504704961",
  "ainvs": [
    "1",
    "0",
    "0",
    "-6846036141864580415461343224",
    "237743716924884102637037303696937775796288"
  ],
  "rank_lower_bound": 5,
  "torsion": [
    8
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  "naive_height": 204.06716933882632,
  "faltings_height": 14.968960439158936,
  "conductor": "916399790245882510302",
  "bad_primes": [
    "2",
    "3",
    "7",
    "19",
    "73",
    "79",
    "97",
    "199",
    "223",
    "359",
    "128857"
  ],
  "discriminant": "-3882402585839414797511646110356470423294879795340961488571892096822008083913516187648",
  "regulator": "485739.624878147792933338167000020544119453272629",
  "points": [
    [
      "-26582546568208",
      "-633201944397337637368"
    ],
    [
      "2024596322851172",
      "91022951659981520271512"
    ],
    [
      "65776693082151506",
      "16869713582173882655604260"
    ],
    [
      "-45826422273095461024/714025",
      "-387630399997951812893481230936/603351125"
    ],
    [
      "33822779890951982/841",
      "4041755866523462414580484/24389"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Voznyy (2021). Source: https://dujella.github.io/tors/z8old5.html (curve entry 31). Published independent points; exact point coordinates checked.",
  "created_at": "2026-09-26 20:25:30",
  "updated_at": "2026-09-26 20:25:30"
}