{
  "id": 3069,
  "curve_key": "37987714761439497258120002981329:-234131327272985575398002007597318267293819236633",
  "ainvs": [
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  "rank_lower_bound": 9,
  "torsion": [
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  "naive_height": 218.14444680457447,
  "faltings_height": 15.812098199360042,
  "conductor": "1408511896423728478584743728713260910",
  "bad_primes": [
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    "5",
    "7",
    "19",
    "23",
    "29",
    "31",
    "47",
    "59",
    "61",
    "131",
    "251",
    "457",
    "6716749848486217"
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  "discriminant": "763391076219577635234188903367807650464648141523228813187565619029178541380183511859200",
  "regulator": "46475065.844877302812819757963399342732183775003694557732",
  "points": [
    [
      "-74068218887962",
      "-18143796961075289154739"
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    [
      "511534686823160",
      "58470570596143399925"
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    [
      "357745618823558",
      "5800567653253786719341"
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    [
      "46172989499126",
      "15314763171500332546349"
    ],
    [
      "355981327890944",
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    [
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    [
      "380819855348144",
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    ],
    [
      "487486341852188",
      "1015429697665547098151"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Kulesz - Stahlke (2001). Source: https://dujella.github.io/tors/z4old9101112.html (curve entry 37). Published independent points; exact point coordinates checked.",
  "created_at": "2026-09-26 20:35:47",
  "updated_at": "2026-09-26 20:35:47"
}