{
  "id": 4644,
  "curve_key": "167715877351271165377542544620095929:-68726259527704724850301192805784018006545820564258733",
  "ainvs": [
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  "rank_lower_bound": 12,
  "torsion": [
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  "family": null,
  "families": [],
  "naive_height": 243.32394220729412,
  "faltings_height": 18.032196065193013,
  "conductor": "2375058682479802063668459948953732228379612270",
  "bad_primes": [
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    "31",
    "151",
    "157",
    "167",
    "173",
    "257",
    "269",
    "2835823128719620893424561"
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  "discriminant": "-3288957625062392082778626427742638161908647190096449186758620057609918487960442920570688144962420900",
  "regulator": "327211501580996.44033190877465696494602871082987477291504582580",
  "points": [
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      "349321523094402491776676412759/4105830901225",
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      "9242717741287208456487/24964",
      "-877893323767517843093557513178749/3944312"
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      "6271869773583154227458767218818813220557436/11461969651044622230428209",
      "15619001331024413218490484523026207522529221948618815168571447674/38805106644037388932217167713235636823"
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      "8654704967459850236/289",
      "-6525485762443353806547239946/4913"
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      "-15497299627748084959682416987697794711522/22886710181440559"
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  "submitter": "Maksym Voznyy",
  "history": [],
  "commentary": "t = 2134/1363 for y^2 + (7t^2+309) x y - 91 (t^2-1)(t^2-25)(t^2-121) y = x^3 from https://github.com/Layr-Labs/elliptic-rank-challenge-public/blob/main/submission/board/3-r12-z3k3.ec",
  "created_at": "2026-10-19 21:57:53",
  "updated_at": "2026-10-19 21:57:53"
}