{
  "id": 2935,
  "curve_key": "5003859321897946833253921:-11299390527575310114710849359121135281",
  "ainvs": [
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    "0",
    "-104247069206207225692790",
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  "rank_lower_bound": 7,
  "torsion": [
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  "naive_height": 170.63562427287312,
  "faltings_height": 12.081938673741012,
  "conductor": "80529780156718252850490",
  "bad_primes": [
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    "3",
    "5",
    "7",
    "11",
    "13",
    "19",
    "23",
    "29",
    "61",
    "1090099",
    "3182189"
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  "discriminant": "-1381107453326274305673116527361670366762486464846925051472469936100000",
  "regulator": "68260.87170051390637158383520048999615737394153661001",
  "points": [
    [
      "116272397230",
      "50287710041280910"
    ],
    [
      "135871495882",
      "37711009485178696"
    ],
    [
      "-209059328720",
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    ],
    [
      "111490681480",
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    [
      "179713181770",
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    [
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      "14333157496354510"
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    [
      "130979046880",
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  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Dujella - Lecacheux (2009). Source: https://dujella.github.io/tors/z5old678.html (curve entry 27). Published independent points; exact point coordinates checked.",
  "created_at": "2026-09-26 20:29:05",
  "updated_at": "2026-09-26 20:29:05"
}