{
  "id": 3138,
  "curve_key": "623079214724427055292872461135427864033:-2363877276582563125587257116866410741810783268684923339345",
  "ainvs": [
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    "1",
    "1",
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  "rank_lower_bound": 11,
  "torsion": [
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    2
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  "naive_height": 267.983211026792,
  "faltings_height": 20.398756251559544,
  "conductor": "13234498274885365856717453272852852367581218",
  "bad_primes": [
    "2",
    "3",
    "7",
    "11",
    "31",
    "37",
    "43",
    "47",
    "71",
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    "199",
    "227",
    "233",
    "431",
    "677",
    "2887",
    "3019",
    "308213"
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  "discriminant": "136752719644102341530239379866831459594304619659879481779262024903654763935704953706649387473658315894439310133504",
  "regulator": "63509074844.0323403290569945165729752344852325417600676303054",
  "points": [
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      "300240628426701938939/1444",
      "-11762235011103428050885603511937/54872"
    ],
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      "3036364435415959774395974519/243204025",
      "-160317966008087905277545188885701256519693/3792766769875"
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      "18763759968802292859468200532171951581715498637343354377065865645601/3276403209278511285496685779045574932995843167296",
      "-63936532686550911163111408379409923934369789793046363724835765545421816443413828778516585865986058731/5930564232238350505738441539298129211170107868389360516460377194229510656"
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      "188861145970638683945069419563224345807058681056721297607004228609845746897598081/49474500433555650038182380345537357782725021065848975585292225",
      "-1032932200576951021884788651897836161839518477884387205454800910585742896418210162633590388129208513470029527856897440099/347994296798410418231495828473052858699494499697213339086673068230153135542677198251568673375"
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  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous image of D-z4old9101112-015, rational kernel x=1851990373201879945. Source: https://dujella.github.io/tors/z4old9101112.html. Independent witness points transported by the degree-2 isogeny. Witnesses saturated by exact rational halves of published and transported relations; quadratic-character independence is certified.",
  "created_at": "2026-09-26 20:39:01",
  "updated_at": "2026-09-26 20:39:01"
}