{
  "id": 2873,
  "curve_key": "77813080834360059115216:-4302379869656106487835404863491264",
  "ainvs": [
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    "-1621105850715834564900",
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  "rank_lower_bound": 6,
  "torsion": [
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  "naive_height": 158.12578951213226,
  "faltings_height": 11.242958606683782,
  "conductor": "174140970298157782920",
  "bad_primes": [
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    "5",
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    "11",
    "13",
    "19",
    "29",
    "31",
    "37",
    "41",
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    "67",
    "109",
    "163"
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  "discriminant": "261943314808113584828175457033067436235611494555073979459539360000",
  "regulator": "8988.4027918010209961788638229313779100335210767938",
  "points": [
    [
      "1291128254",
      "1699618513398080"
    ],
    [
      "-9589966542",
      "4432154369225880"
    ],
    [
      "-166732650939/4",
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    ],
    [
      "-987086238936/25",
      "340817455790473662/125"
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    [
      "6033839983202",
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    [
      "-14560799125208/3721",
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  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Ansaldi - Ford - George - Mugo - Phifer (2005). Source: https://dujella.github.io/tors/z2z4old678.html (curve entry 72). Published independent points; exact point coordinates checked.",
  "created_at": "2026-09-26 20:26:18",
  "updated_at": "2026-09-26 20:26:18"
}