{
  "id": 522,
  "curve_key": "4588857299175629852815472192880094927568529814693087825:-9681912571648307772113424605241619378170860630493515657836429676453135471959345625",
  "ainvs": [
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    "1",
    "1",
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    "11205917328296652514020167327343969484205598072196150707448747360751344747408781"
  ],
  "rank_lower_bound": 17,
  "torsion": [
    2
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  "naive_height": 377.58967818098597,
  "faltings_height": 29.349101985323138,
  "conductor": "132427244033169534332852238392107081376038339664432536271108120645163730957223993769897688950",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "17",
    "31",
    "61",
    "233",
    "521",
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    "757",
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    "2029",
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    "3001",
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    "16981",
    "32413",
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    "346361",
    "393103",
    "604697",
    "5987573",
    "15191747"
  ],
  "discriminant": "1672999032487882401600002297691034484154256063982955395004797489537210681366640681503241840336803431618425255372403228999940038083464389977656159178326016000000",
  "regulator": "129742692587123759061163116.247289465484688040297560525589595356949177241",
  "points": [
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      "156571848725180775412346645722659547050132062742574258/6259005167589"
    ],
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      "6862446495868157160971225548355/22201",
      "11065018236127042770562741021700489481839504178/3307949"
    ],
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      "-7480147558863083418513373127100251209165/47296278718441",
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      "49818206914222594725463042440176008209379/239126790875625",
      "2128288292844129711985800153111018251614279609495561491385042/3697790934233174203125"
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      "265520712280085752117529130046217053801281780354848255274759658805902/11791667490506959583823931"
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      "10895841283945353202318821877239270157851559305241835/405228154309545511201121089",
      "23998181861667877805864792611106084378168261246730565495409480202333914041752054/8157356023236244167036051795827454694687"
    ],
    [
      "12178100143627147345907656830050848835693755/115984002247906081",
      "60236348308121718220062684979170837060669344873869662838626462362/39500003693700428315049521"
    ],
    [
      "17014001794362800144846696773899720564746795/41023021549539649",
      "54419274069746417928867197799242117112583644999167473686787133046/8308860504035080710746143"
    ],
    [
      "59241093984320983764046395387906939372865/4157590326289",
      "14415614974353020206567342241429351555748280955599987973998516/8477397354338817913"
    ],
    [
      "-9043959272602262167324615965877355285/55722907249",
      "62320114739186389786449298222353778136191280642112823226/13153782316477193"
    ]
  ],
  "submitter": "Matthias Breddin",
  "history": [],
  "commentary": "Exact rank 17, unconditional: rational 2-torsion point, 17 independent points (Neron-Tate height matrix of rank 17; the archived certificate additionally saturates the lattice at all primes up to 97 — the points listed here are the ellrank output, not the saturated basis) with matching 2-descent upper bound 17 (PARI/GP 2.15.4 ellrank, effort 2). Fiber t=106/7989 on branch u=58/37 of the Elkies-Klagsbrun Z/2Z rank-9 family (arXiv:2003.00077), found by a Mestre-Nagao residue-table sieve followed by an exact 2-descent-type upper bound and ellrank (Matthias Breddin, 2026-09-02; method: doi:10.5281/zenodo.22242107).",
  "created_at": "2026-09-02 13:42:59",
  "updated_at": "2026-09-02 13:42:59"
}