{
  "id": 2853,
  "curve_key": "46012576403300268165545992456686081808:-312115133944248555257720640302716604456051655226144412096",
  "ainvs": [
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  "rank_lower_bound": 5,
  "torsion": [
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  "naive_height": 260.1659343209385,
  "faltings_height": 18.65519199060757,
  "conductor": "317396988702234542237136",
  "bad_primes": [
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    "7",
    "11",
    "13",
    "17",
    "19",
    "37",
    "79",
    "109",
    "197",
    "479",
    "680249"
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  "discriminant": "453049812292754972368990024286652146861505188926279744886362970642279992907854559232",
  "regulator": "3778524.01294338643340287431970468299303754945398",
  "points": [
    [
      "565237601212634066",
      "44042207341351033713822"
    ],
    [
      "2523381863043230225154/961",
      "118971517062884738300429680991230/29791"
    ],
    [
      "1051191516438152794722/1849",
      "336559033269697808566620450694/79507"
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    [
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    [
      "597965350847321449658258/923521",
      "97292468679453797994982752355479138/887503681"
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  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Dujella - Kazalicki - Peral (2021). Source: https://dujella.github.io/tors/z8old5.html (curve entry 59). Published independent points; exact point coordinates checked.",
  "created_at": "2026-09-26 20:25:22",
  "updated_at": "2026-09-26 20:25:22"
}