{
  "id": 2916,
  "curve_key": "25585159989017366199929281:-129725765187623790623748763803334876321",
  "ainvs": [
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  "rank_lower_bound": 7,
  "torsion": [
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  "naive_height": 175.51697214311673,
  "faltings_height": 12.432837348238325,
  "conductor": "4290426777866593139490",
  "bad_primes": [
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    "3",
    "5",
    "11",
    "13",
    "17",
    "23",
    "29",
    "31",
    "41",
    "101",
    "113",
    "373",
    "16301"
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  "discriminant": "-46711743185348559156914365269279728565638561159211350855833734375000000",
  "regulator": "25290.20144692118189331265185275928133539878192244612",
  "points": [
    [
      "225881035820",
      "203151228866431340"
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    [
      "-199633635190",
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    ],
    [
      "379553028866",
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    [
      "268669162916",
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    [
      "329053583870",
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      "316093339430",
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    [
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  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Eroshkin (2007). Source: https://dujella.github.io/tors/z6old678.html (curve entry 129). Published independent points; exact point coordinates checked.",
  "created_at": "2026-09-26 20:28:14",
  "updated_at": "2026-09-26 20:28:14"
}