{
  "id": 2912,
  "curve_key": "28697866170878107053293409121:-5981172629719717402725166424278477262056081",
  "ainvs": [
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  "rank_lower_bound": 7,
  "torsion": [
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  "naive_height": 196.99438109283065,
  "faltings_height": 14.419230223818412,
  "conductor": "142464282826190789129133930",
  "bad_primes": [
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    "3",
    "5",
    "7",
    "11",
    "17",
    "19",
    "37",
    "41",
    "353",
    "34231",
    "10416255431"
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  "discriminant": "-7025344603942946062994327764270921215295942312854190594956277175699278322073600000",
  "regulator": "418862.2959604844069834516978853757170106745884804016",
  "points": [
    [
      "136948832900",
      "82708996863243207710"
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    [
      "12658290255380",
      "37187096661453156110"
    ],
    [
      "-8085873615820",
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    [
      "1502180413580",
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    [
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    [
      "13688354493380",
      "36104952169567028510"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Dujella - Lecacheux (2009). Source: https://dujella.github.io/tors/z5old678.html (curve entry 21). Published independent points; exact point coordinates checked.",
  "created_at": "2026-09-26 20:28:03",
  "updated_at": "2026-09-26 20:28:03"
}