{
  "id": 3073,
  "curve_key": "3028854606335958875580348736:-165319028449082120355139695796000929833984",
  "ainvs": [
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    "-1",
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    "-63101137631999143241257265",
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  "rank_lower_bound": 9,
  "torsion": [
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  "naive_height": 189.8339461235487,
  "faltings_height": 13.676339410023978,
  "conductor": "25329868104284268623200965514080",
  "bad_primes": [
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    "3",
    "5",
    "11",
    "13",
    "23",
    "29",
    "31",
    "41",
    "43",
    "53",
    "59",
    "67",
    "83",
    "582150181451"
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  "discriminant": "264010719034448686848336190538563616324955649278495244881276251650449600000000",
  "regulator": "397881275.61053330737815647226735091379561742342369116155",
  "points": [
    [
      "4046893030649",
      "1501755661273561980"
    ],
    [
      "-207449533823",
      "14297651626859442556"
    ],
    [
      "-325725187176",
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    [
      "3981277360529",
      "1795508458242684900"
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    [
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    [
      "-2910887979271",
      "18717827725126791300"
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  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Eroshkin (2008). Source: https://dujella.github.io/tors/z4old9101112.html (curve entry 43). Published independent points; exact point coordinates checked.",
  "created_at": "2026-09-26 20:35:58",
  "updated_at": "2026-09-26 20:35:58"
}