{
  "id": 2927,
  "curve_key": "7243013948838190043698189681:-729564299469909468005907181882159524988297",
  "ainvs": [
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    "0",
    "0",
    "-150896123934128959243712285",
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  "rank_lower_bound": 7,
  "torsion": [
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  "naive_height": 192.78653226536622,
  "faltings_height": 14.05950671485697,
  "conductor": "66962884494658686917988066",
  "bad_primes": [
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    "3",
    "7",
    "11",
    "17",
    "19",
    "41",
    "67",
    "937",
    "2729",
    "63883377511"
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  "discriminant": "-88128758007951727700623417517995188168956420423430962364900089911158511036563456",
  "regulator": "1901912.265124174075667012772353512424460983016866205",
  "points": [
    [
      "6185569421986",
      "12152873534380947055"
    ],
    [
      "7399018466710",
      "11531808471208398823"
    ],
    [
      "6877371129730",
      "11485726171880266063"
    ],
    [
      "5996702988790",
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    ],
    [
      "3438036957610",
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    [
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    [
      "-13501730569340",
      "-20504642078577659777"
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  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Dujella - Lecacheux (2009). Source: https://dujella.github.io/tors/z5old678.html (curve entry 20). Published independent points; exact point coordinates checked.",
  "created_at": "2026-09-26 20:28:43",
  "updated_at": "2026-09-26 20:28:43"
}