{
  "id": 2934,
  "curve_key": "384356071965614146428572161:752299001981307936928704696092657788159",
  "ainvs": [
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  "rank_lower_bound": 7,
  "torsion": [
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  "naive_height": 183.64083487661603,
  "faltings_height": 13.37103505291075,
  "conductor": "548088118837830139058490",
  "bad_primes": [
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    "7",
    "11",
    "13",
    "19",
    "23",
    "29",
    "31",
    "37",
    "47",
    "59",
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    "349",
    "21269"
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  "discriminant": "32531719420690972430975073726625714253395169331067396996901012701593600000000",
  "regulator": "61425.19430451141561932310202945296386394655112896947",
  "points": [
    [
      "-383181597927",
      "-1463323767915288287"
    ],
    [
      "3563438686053",
      "3980478568219330213"
    ],
    [
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    [
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    [
      "3335717042133",
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  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Eroshkin (2008). Source: https://dujella.github.io/tors/z2z4old678.html (curve entry 67). Published independent points; exact point coordinates checked.",
  "created_at": "2026-09-26 20:29:01",
  "updated_at": "2026-09-26 20:29:01"
}