{
  "id": 3056,
  "curve_key": "924895261800974195240285640107689:-28127998605916697169289643130157000248302499409813",
  "ainvs": [
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  "rank_lower_bound": 8,
  "torsion": [
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  "naive_height": 227.72169987131193,
  "faltings_height": 16.290627562730744,
  "conductor": "1537557927687420856077617546790",
  "bad_primes": [
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    "29",
    "41",
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    "59",
    "61",
    "73",
    "83",
    "107",
    "127",
    "977",
    "182057"
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  "discriminant": "1027587137130271525920944449534041253598570604442581009178061565013457188476786339600",
  "regulator": "6973135.36811254893874616314914227735354294620759989747",
  "points": [
    [
      "2140883341156045",
      "33408148409468593971467"
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    [
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      "45331337312131766243"
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    [
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    [
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    [
      "4318476084514441",
      "172860121954632936055307"
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  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Dujella - Peral - Tadic (2019). Source: https://dujella.github.io/tors/z6old678.html (curve entry 25). Published independent points; exact point coordinates checked.",
  "created_at": "2026-09-26 20:35:13",
  "updated_at": "2026-09-26 20:35:13"
}