{
  "id": 3091,
  "curve_key": "433688732233874384365327441:-8926062153499555855559762478455568346489",
  "ainvs": [
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  "rank_lower_bound": 10,
  "torsion": [
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  "naive_height": 184.00310790542176,
  "faltings_height": 13.205603149018364,
  "conductor": "12619320802739804855437753113854835",
  "bad_primes": [
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    "199",
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    "4396001"
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  "discriminant": "1097313133865711912941521070855065466307654513728837769895080511232128515625",
  "regulator": "2729169860.541515073714011677527520629114220998646795720695",
  "points": [
    [
      "-1192655789981",
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    [
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    [
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    [
      "1504053209435011/25",
      "58258911526403305422326/125"
    ],
    [
      "7863439448351/4",
      "3263960924390316949/8"
    ],
    [
      "40714222883260469/26896",
      "1545195960311326667536447/4410944"
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  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Dujella - Kulesz (2001). Source: https://dujella.github.io/tors/z2z2old1011121314.html (curve entry 64). Published independent points; exact point coordinates checked.",
  "created_at": "2026-09-26 20:36:51",
  "updated_at": "2026-09-26 20:36:51"
}