{
  "id": 3035,
  "curve_key": "34752801819891523731653077532881:190731015843250980669885060439969899429249146471",
  "ainvs": [
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    "0",
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  "rank_lower_bound": 8,
  "torsion": [
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  "naive_height": 217.8774389594774,
  "faltings_height": 16.111782275999662,
  "conductor": "11357092358577020158149155010",
  "bad_primes": [
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    "5",
    "11",
    "37",
    "43",
    "47",
    "101",
    "149",
    "223",
    "283",
    "359",
    "379",
    "3561661"
  ],
  "discriminant": "3237631601102205186043641271090357682445986706978419682843007813332700118176619298816000000",
  "regulator": "91358222.9944397643111920916191657495565926732105942749",
  "points": [
    [
      "-394226023171526",
      "-1845109664794335908447"
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    [
      "-405292302390506",
      "-2472011746215283313507"
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    [
      "983835558752934",
      "4383998879741211236733"
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    [
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    ],
    [
      "1058161029785734",
      "14069405815261419929533"
    ],
    [
      "696116936708208076/9",
      "580760291708194905583202621/27"
    ],
    [
      "26824447802498614",
      "4391117855252108880847213"
    ],
    [
      "14301405513797491/4",
      "1656885557501400892736399/8"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Dujella - Peral (2020). Source: https://dujella.github.io/tors/z6old678.html (curve entry 52). Published independent points; exact point coordinates checked.",
  "created_at": "2026-09-26 20:34:18",
  "updated_at": "2026-09-26 20:34:18"
}