{
  "id": 3140,
  "curve_key": "10514203433066185595917777021961497787521:-828066987376555981466761398787236466166745916471858255999681",
  "ainvs": [
    "1",
    "0",
    "0",
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    "958410865019162015568275571339857856218598670068189825600"
  ],
  "rank_lower_bound": 11,
  "torsion": [
    2,
    2
  ],
  "naive_height": 276.4606370332716,
  "faltings_height": 21.054341229851833,
  "conductor": "4669857800272842393315326009855704719253530",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "13",
    "17",
    "19",
    "31",
    "37",
    "79",
    "89",
    "109",
    "113",
    "439",
    "4261",
    "5407",
    "8623",
    "673273",
    "907969"
  ],
  "discriminant": "275829981192542281284106419027755867172166346251235478954302611638302002084657762519350331279924599958856077731840000",
  "regulator": "136960623034.415051630882489844306463521332971096787326059165",
  "points": [
    [
      "22946100749107332760",
      "-89519962308669705395021397440"
    ],
    [
      "161210193274893466219990/1849",
      "63835569167590725724324068964169170/79507"
    ],
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      "157358382742855280216782673014/91145209",
      "62419301883746200225979830369632964534499506/870163310323"
    ],
    [
      "93578514918251210879804294416/1040772121",
      "28254879610656986582110210795260339410453192/33576349395581"
    ],
    [
      "16994519255154003772703896848935886265/1365006803078523136",
      "-20242074679108022835294721287742214865532366120837319515/1594785299715127300495855616"
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      "1377416906644057351110912019960/7486921729",
      "-1611468777868612351103239708409775095246882600/647820876445183"
    ],
    [
      "88681025525334772480",
      "-823983943048634005448394875240"
    ],
    [
      "2020720755336739252998593603440/907452475609",
      "18972090142362962395117905870892924067284589560/864441950622560227"
    ],
    [
      "122119946063228656458210712982650153291974685526521712961228090234242137/1665800886854889197297269435384175649500355838116096",
      "-41849865565604860265036695267222058856852649360890414659538867247320043086526566211520058857885601085322293/67988370660645068620355671860457273738835233256052106382841357974204404985856"
    ],
    [
      "29948659568239998365903129723952131979062381680/342769537144770775464923521",
      "-5111698276434158190596859883141431757481841502375710500648571939553640/6346047625711861124320242653214567722431"
    ],
    [
      "1869383131380531799476867415/139570596",
      "-34085539116048654194565345345655928425885/1648887021144"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous image of D-z4old9101112-016, rational kernel x=8316639696921356080. 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 20:39:09",
  "updated_at": "2026-09-26 20:39:09"
}