{
  "id": 3033,
  "curve_key": "27494524781956111424025807503633296:-4560186643880920473146516342990272289761523174549656",
  "ainvs": [
    "0",
    "1",
    "1",
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    "5277993800788102208540934781543522853711433047164"
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  "rank_lower_bound": 8,
  "torsion": [
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  "naive_height": 237.89840659212126,
  "faltings_height": 17.551443460058067,
  "conductor": "12162741732981505634646926333085",
  "bad_primes": [
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    "5",
    "7",
    "11",
    "13",
    "41",
    "53",
    "59",
    "79",
    "383",
    "208818294867814661"
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  "discriminant": "-6276999389525198150292437288436716172134508313702541801423357921959469631161448729511210341796875",
  "regulator": "27009174.4520971544696180490494615379011395167899902511",
  "points": [
    [
      "13539127696772711",
      "67649036229802681341187"
    ],
    [
      "5519370865025336",
      "1511496915505795364744812"
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    [
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      "2512696806602195467066312"
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    [
      "12104774610988001",
      "343520619135864160480717"
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    [
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      "2631795889070645474955277"
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    [
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      "165325664289917783157187"
    ],
    [
      "13455153700979036",
      "82361590308906363191587"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Dujella - Lecacheux - Petricevic (2021). Source: https://dujella.github.io/tors/z5old678.html (curve entry 11). Published independent points; exact point coordinates checked.",
  "created_at": "2026-09-26 20:34:10",
  "updated_at": "2026-09-26 20:34:10"
}