{
  "id": 4110,
  "curve_key": "158310511269553411416781428050484789684281005333456:477603968034506273360517357768342160354092680069595365381670004046026107200",
  "ainvs": [
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    "-552782370410308186759859152351168724160371736988615356817601978856548736"
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  "rank_lower_bound": 20,
  "torsion": [
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  "naive_height": 346.7659284880244,
  "faltings_height": 26.961812561867177,
  "conductor": "322603758958242647542220542271392585593818068317511565892515943705988412227992083496",
  "bad_primes": [
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    "7",
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    "37",
    "61",
    "71",
    "173",
    "211",
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    "50929",
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  "discriminant": "2164066545967320003799831059294966185795791012526771695944070906751480849488913142941672562125528564216304700349541352221842002815301817544885487872",
  "regulator": "10936340962246599755381.2578200802897532657729512660123768339512962299292081028",
  "points": [
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      "-197803862920588554635166",
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      "2152982776371883318632336",
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      "2339481037691685745255419",
      "2129711908625992478344101130797202992"
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      "-1473686790343775639184426",
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      "8056845593317710639547181/4",
      "7902715038875248431961255637615211099/8"
    ],
    [
      "73026275212600403333847165/4",
      "620925298225676853622165220709904947939/8"
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      "6948350068445452699264433376",
      "579191955556212570459790441602665102568144"
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      "-2460885766150250062038910614/1681",
      "73525686329937471280038629348704718662926/68921"
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  "submitter": "wgxli",
  "history": [],
  "commentary": "specialization at T = 12131/8109 of the rank-9 fibration of X1008 given by:\ny^2 + (105912T^2 - 91132T - 6860)xy = x(x + (5T - 257)(27T + 41)(223T + 139)(3115T + 577))(x + (707T - 6214)(37T + 26)(135T + 47)(703T + 139)).",
  "created_at": "2026-10-09 15:25:23",
  "updated_at": "2026-10-09 15:25:23"
}