{
  "id": 3485,
  "curve_key": "2584372027115355971736594948123261851425:-131363192861715770308904830515030617013511077217800575640625",
  "ainvs": [
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  ],
  "rank_lower_bound": 17,
  "torsion": [
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  "naive_height": 272.2509035270005,
  "faltings_height": 20.392815624051803,
  "conductor": "3633958535429087440559985546561230089154484056735382962822667450",
  "bad_primes": [
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    "3",
    "5",
    "11",
    "13",
    "19",
    "29",
    "37",
    "53",
    "73",
    "109",
    "131",
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    "419",
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    "727",
    "1097",
    "2953",
    "3529",
    "5009",
    "28751",
    "110629",
    "327499"
  ],
  "discriminant": "2706872560514487077203613393909313786743701775469765738912067598155820590361412155618692440070651048663104000000",
  "regulator": "24565558987733038019152.7202217331736510367272780842250582717652251691882",
  "points": [
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      "21900930456404710104591694598978918586/1256216039"
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      "477548328864233486977033084104/38803090225",
      "281203507561078797192609597434904825646550238/7643626727971625"
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      "1782972684410882486102975668815027064626964320/2731137071502346129"
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      "4497791835397316855343558730552596/627663381410521",
      "182161395677868565848488729058482704431049376320230/15724983131451260232931"
    ],
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      "5240980104291669418608357119239068/484157664837889",
      "308331551486467429448202420231897351071842696612278/10653203363346672156287"
    ],
    [
      "15165488900656768857840906840162732/7326413123391961",
      "4410280808249198865392758173263011419775820781782946/627100440971366380663709"
    ]
  ],
  "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=720/73. 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): 17 independent points, 2-Selmer upper bound 17.",
  "created_at": "2026-09-27 09:39:58",
  "updated_at": "2026-09-27 09:39:58"
}