{
  "id": 2843,
  "curve_key": "686807057214828710844560702313601:-17999155255357583277024551766619336684922316830401",
  "ainvs": [
    "1",
    "0",
    "0",
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    "20832355619626831304182830954139201872779240000"
  ],
  "rank_lower_bound": 5,
  "torsion": [
    8
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  "naive_height": 226.82881858288192,
  "faltings_height": 16.329816976920974,
  "conductor": "344341391147749705710",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "23",
    "41",
    "71",
    "191",
    "271",
    "311",
    "10639"
  ],
  "discriminant": "446126168951856068263041717922777514876517999410934122561810051704892034179097600000000",
  "regulator": "53285.3925724629411689783202722754305883064597569",
  "points": [
    [
      "1211191369036400",
      "72655671639587522661800"
    ],
    [
      "2184005996951920",
      "5205662428129388200"
    ],
    [
      "1791360394830560",
      "30808050954630647143400"
    ],
    [
      "2718620200653680",
      "45011891361086352564200"
    ],
    [
      "1332000953825150",
      "64317318766862744365550"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Dujella - MacLeod - Peral (2013). Source: https://dujella.github.io/tors/z8old5.html (curve entry 12). Published independent points; exact point coordinates checked.",
  "created_at": "2026-09-26 20:24:56",
  "updated_at": "2026-09-26 20:24:56"
}