{
  "id": 3064,
  "curve_key": "0:-611963763325802002990274400",
  "ainvs": [
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    "0",
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    "708291392738196762720225"
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  "rank_lower_bound": 8,
  "torsion": [
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  "naive_height": 123.35743060472893,
  "faltings_height": 8.337441792852374,
  "conductor": "76495470415725250373784300",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "17",
    "29",
    "41",
    "47",
    "59"
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  "discriminant": "-216724333115670259601781304169912713587581589870000",
  "regulator": "327055.732652397001629942270651692262565342990579299244",
  "points": [
    [
      "-88860785",
      "81396479060"
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    [
      "-87348261",
      "204569627262"
    ],
    [
      "-63256830",
      "674665720365"
    ],
    [
      "-40588401",
      "800890328532"
    ],
    [
      "126513660",
      "1653248880465"
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    [
      "101707060",
      "1326794024465"
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    [
      "-29810690",
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    [
      "-44793980",
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  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Elkies - Rogers (2003). Source: https://dujella.github.io/tors/z3old891011121314.html (curve entry 65). Published independent points; exact point coordinates checked.",
  "created_at": "2026-09-26 20:35:36",
  "updated_at": "2026-09-26 20:35:36"
}