{
  "id": 3489,
  "curve_key": "127369789348040991489372020456999425:-45254591395521426005238411854843167452733321036410625",
  "ainvs": [
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    "0",
    "0",
    "-2653537278084187322695250426187488",
    "52377999300372020618268203510163981734577882350592"
  ],
  "rank_lower_bound": 16,
  "torsion": [
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  "naive_height": 242.49720795463588,
  "faltings_height": 18.039169593714227,
  "conductor": "53400310113364992979902636017282809299958520515445675366550",
  "bad_primes": [
    "2",
    "3",
    "5",
    "13",
    "23",
    "29",
    "47",
    "53",
    "71",
    "109",
    "139",
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    "1117",
    "2029",
    "5147",
    "5581",
    "6577",
    "6709",
    "9173",
    "16553"
  ],
  "discriminant": "10619273669146597002015035527198923831893959421490517772149249777782601827954241999666235572224000000",
  "regulator": "2964822413952052555619.350218395606473779504030882205180920303201487044",
  "points": [
    [
      "112218440801456419/4",
      "971239976528185947279215/8"
    ],
    [
      "-1481731459068902970853232/30283009",
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      "210482485171580879011823872/6695985241",
      "89314302788478751769009086476486914656/547925776285789"
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      "196086490592611908219909070912/6049430474481",
      "9672399594861375706457598418884264202812896/14878931168384013879"
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      "309000117219521927362787610688/9852272601889",
      "2195509381446608871632579240394792956802848/30924638367805055537"
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    [
      "539635754564083630100319416386/15011897481361",
      "107905907814189819652670788149323231453904196/58163882017585340359"
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    [
      "606777413127470774157204679648/29176342689169",
      "392017413119854012348299619937786086856416288/157596394328001312697"
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    [
      "139840260922877615799398949014940667/635723733510705316",
      "50971646319298486405843313372819287545932522406156641/506877061558291002106091864"
    ],
    [
      "43334586209616100125137682447450784/1592322804383871169",
      "1134985981039241716381685216515822971204005062590752/2009308735355391110681419553"
    ]
  ],
  "submitter": "Steps Unbounded",
  "history": [],
  "commentary": "Z/2Z curve from the Elkies-Klagsbrun rank-9 family y^2=x^3+2A(t,u)x^2+B(t,u)x (Elkies-Klagsbrun 2020), fibre u=11/5, t=45/901. Found by sweeping t=a/b with the lossless conic-Hilbert prefilter of Breddin (Zenodo 10.5281/zenodo.22242109), screened with PARI ellrank (2-descent): 16 independent points, 2-Selmer upper bound 16.",
  "created_at": "2026-09-27 10:22:20",
  "updated_at": "2026-09-27 10:22:20"
}