{
  "id": 3049,
  "curve_key": "2676997598610661239322183324321:-36154532912737689443345213035590675754240369",
  "ainvs": [
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    "0",
    "-55770783304388775819212152590",
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  "rank_lower_bound": 8,
  "torsion": [
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  "naive_height": 210.18674597194268,
  "faltings_height": 15.583798436909884,
  "conductor": "40671677445041477433310596010",
  "bad_primes": [
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    "5",
    "7",
    "19",
    "23",
    "29",
    "37",
    "53",
    "107",
    "131",
    "239",
    "263",
    "3329",
    "7971031"
  ],
  "discriminant": "11101217566758100654949756159762288423826424014600317105422493292781497158753450983424000",
  "regulator": "22698361.3937660874445369616515514824338013522908709259",
  "points": [
    [
      "306541429369044",
      "3427939023665242824898"
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    [
      "527877698364",
      "111380063363099860258"
    ],
    [
      "244334067358908",
      "1000837542844271276066"
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    [
      "258256536657212",
      "1692178187168780721570"
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    [
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    [
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    ],
    [
      "-141999532315716",
      "-2257877463627263982302"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Dujella - Peral (2020). Source: https://dujella.github.io/tors/z6old678.html (curve entry 66). Published independent points; exact point coordinates checked.",
  "created_at": "2026-09-26 20:34:55",
  "updated_at": "2026-09-26 20:34:55"
}