{
  "id": 3108,
  "curve_key": "50917581562369839804594040724950481425196491909573174401:-363329109788328971761632543319635917007922532503227929660266372962174856654077521601",
  "ainvs": [
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  "rank_lower_bound": 11,
  "torsion": [
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    2
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  "naive_height": 384.809409898177,
  "faltings_height": 29.66673256458838,
  "conductor": "2603348955675569045873307484526694064917261974747900874693810",
  "bad_primes": [
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    "1951",
    "3457",
    "14008947836626425239"
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  "discriminant": "512528915611657524637710374768288075919700064229683424846841011607507715694302155250803756901555862053112766475767218160083261220971276882971354228178576000000",
  "regulator": "331838289473254.499228422681649951649090171842401136490151528",
  "points": [
    [
      "692624334898482291199048909",
      "4250568232561562704733904331849250374318"
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      "-345592066525454767124899692434134347159109856549477867126/1235476185330203389"
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      "32872782689454871815787627899982428901047108564526161644522/58227450524016857"
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    [
      "153279794220595517662364047036137/118336",
      "-1421689830259902262808225917192080461333868022831/40707584"
    ],
    [
      "275130737257725277715879172725263971751/366650837289",
      "1522883401322519725154430602121015600491643271479645271334/222013315042723413"
    ],
    [
      "84401229115329331484935298674651128342074463/118073169798066289",
      "-212767298180201410638219461980841470492085806116130025249088514942/40572038948623379144156663"
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    [
      "5094421144436612630554906383576863299802372296192331757413872557/8537045762208871153966935693260991961",
      "-2011407126029310492663560264599158255249840998956499305404474643372276229907891453585149308214/24943730990103314694843612009754080320811192815217736291"
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  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous image of D-z4old9101112-009, rational kernel x=-296874251695587001057277733. 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 20:37:40",
  "updated_at": "2026-09-26 20:37:40"
}