{
  "id": 3044,
  "curve_key": "97684810129097457685813734178081:-967056707698522512281852338668837252366414802225",
  "ainvs": [
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    "0",
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  "rank_lower_bound": 8,
  "torsion": [
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  "naive_height": 220.98117264276127,
  "faltings_height": 16.206816380990944,
  "conductor": "251917139582171073862154486898",
  "bad_primes": [
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    "3",
    "11",
    "13",
    "17",
    "19",
    "23",
    "31",
    "41",
    "43",
    "53",
    "43272041",
    "315313681"
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  "discriminant": "-1770110213594331323167102207328513150861043856231378625553756998094394761298316431442608128",
  "regulator": "35387016.0825821287290435053665230097073506364572475709",
  "points": [
    [
      "809950927023548",
      "1513839045447279408794"
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    [
      "-446118717105622",
      "-44027122021549503042712"
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    [
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    [
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    [
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    [
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      "1308559533193737710183210"
    ],
    [
      "716892025238444",
      "5363468406693209966186"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Dujella - Lecacheux - Petricevic (2021). Source: https://dujella.github.io/tors/z5old678.html (curve entry 10). Published independent points; exact point coordinates checked.",
  "created_at": "2026-09-26 20:34:40",
  "updated_at": "2026-09-26 20:34:40"
}