{
  "id": 3055,
  "curve_key": "-593796712099654074519666218111:-1550927819139490803040206346654937158099228993",
  "ainvs": [
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    "0",
    "0",
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    "1795055346226263534415826963120427011109440"
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  "rank_lower_bound": 8,
  "torsion": [
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  "naive_height": 208.11036505914223,
  "faltings_height": 15.409851185112698,
  "conductor": "29700487374913942444634217870",
  "bad_primes": [
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    "5",
    "11",
    "13",
    "17",
    "19",
    "23",
    "53",
    "83",
    "139",
    "163",
    "283",
    "401",
    "859",
    "95917"
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  "discriminant": "-1513163527746780070164665422564022377930991838214347310087572831655175842583509183426560",
  "regulator": "41445186.6844584197950465450100264613192219531398431283",
  "points": [
    [
      "-56977005345494",
      "-951439538990147868830"
    ],
    [
      "-88177687531336",
      "-136460691923638786600"
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    [
      "61269766750790",
      "1668237052561641052790"
    ],
    [
      "57375133290296",
      "1641250460574949681904"
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    [
      "3414484775543894",
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    [
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    [
      "279283600210559/4",
      "13854482876787646623025/8"
    ],
    [
      "-3211280688799924/49",
      "-287556207376563099439660/343"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Dujella - Peral (2020). Source: https://dujella.github.io/tors/z6old678.html (curve entry 50). Published independent points; exact point coordinates checked.",
  "created_at": "2026-09-26 20:35:10",
  "updated_at": "2026-09-26 20:35:10"
}