{
  "id": 3105,
  "curve_key": "1323678982839846967387369:-1494646669501190853344370344202852853",
  "ainvs": [
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    "-27576645475830145153904",
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  "rank_lower_bound": 10,
  "torsion": [
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  "naive_height": 166.62737159964888,
  "faltings_height": 11.778315432797669,
  "conductor": "37170593689294827178345012036890",
  "bad_primes": [
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    "3",
    "5",
    "7",
    "31",
    "43",
    "53",
    "59",
    "103",
    "283",
    "877",
    "1291",
    "1987",
    "4507",
    "143677"
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  "discriminant": "49354028070902313727986851150097145882968090702338739044656272284100",
  "regulator": "161937424.7065436544686495138371509763343477572993284333770",
  "points": [
    [
      "701564334429",
      "572439898182939937"
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    [
      "202305800739",
      "66564890849359843"
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    [
      "-182192216332",
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    [
      "278734730043",
      "125295900226327393"
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    [
      "162942170538",
      "39530360962167883"
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    [
      "1485480872781/25",
      "2169098217958859489/125"
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    [
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    [
      "155600970168",
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    [
      "617285342297925/5776",
      "807886298510133737857/438976"
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  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Dujella - Kulesz (2006). Source: https://dujella.github.io/tors/z2z2old1011121314.html (curve entry 81). Published independent points; exact point coordinates checked.",
  "created_at": "2026-09-26 20:37:32",
  "updated_at": "2026-09-26 20:37:32"
}