{
  "id": 3039,
  "curve_key": "1251057035010094252324216124765281:-43319064407445042347040543587111694890962036450321",
  "ainvs": [
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  "rank_lower_bound": 8,
  "torsion": [
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  "naive_height": 228.6278906723516,
  "faltings_height": 16.95077822759458,
  "conductor": "1787522945026386872439824060190",
  "bad_primes": [
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    "269",
    "2129",
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  "discriminant": "47189063435064566192444373364955256022383533696190718925593009747696137495697251989927362560000",
  "regulator": "2315386.00748038473679747882929878122023278042626632556",
  "points": [
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      "121543778319648659823190"
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    [
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      "112714350004850071796590"
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    [
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    [
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      "-294692062672567991257160"
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  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Dujella - Peral (2019). Source: https://dujella.github.io/tors/z2z4old678.html (curve entry 17). Published independent points; exact point coordinates checked.",
  "created_at": "2026-09-26 20:34:29",
  "updated_at": "2026-09-26 20:34:29"
}