{
  "id": 2930,
  "curve_key": "4785281004238883342834315281:-317417760645292473413365568346081230675321",
  "ainvs": [
    "1",
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    "-99693354254976736309048235",
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  "rank_lower_bound": 7,
  "torsion": [
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  "naive_height": 191.20602678026572,
  "faltings_height": 13.863823492364553,
  "conductor": "23959330209511704615223770",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "17",
    "19",
    "23",
    "31",
    "41",
    "43",
    "97",
    "193",
    "241",
    "2087",
    "2713"
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  "discriminant": "5106310644853957469804174516316205640090151672922763521755210984300846120960000",
  "regulator": "442159.1380330481429920975426283075068146906381826735",
  "points": [
    [
      "-835742939437",
      "-21215935717377581002"
    ],
    [
      "3746954832963",
      "6814774952116046038"
    ],
    [
      "-6096171578085",
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    [
      "-2303622473757",
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    [
      "2494935489403",
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    [
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    ],
    [
      "7012677573523",
      "3623709821741193398"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Dujella (2005). Source: https://dujella.github.io/tors/z2z4old678.html (curve entry 54). Published independent points; exact point coordinates checked.",
  "created_at": "2026-09-26 20:28:50",
  "updated_at": "2026-09-26 20:28:50"
}