{
  "id": 5923,
  "curve_key": "4079323568865449818258081:-399102103370934214148875198965721523729",
  "ainvs": [
    "1",
    "1",
    "1",
    "-84985907684696871213710",
    "461923730753360670395959152884357162"
  ],
  "rank_lower_bound": 9,
  "torsion": [
    4
  ],
  "family": null,
  "families": [],
  "naive_height": 177.76456126022384,
  "faltings_height": 12.871444558233861,
  "conductor": "2121981965976696746916052177755",
  "bad_primes": [
    "3",
    "5",
    "7",
    "13",
    "17",
    "29",
    "31",
    "41",
    "179",
    "619",
    "1931",
    "15749",
    "19889",
    "37019"
  ],
  "discriminant": "-92138081815933657360854815158223951341170659414872067017328998421075049375",
  "regulator": "343680662461.52623192219572102197954797644021527043350434",
  "points": [
    [
      "-1564953957006123960621871287/2119571842060864",
      "34108875331530137680031874645040492358017/97582561078846442010112"
    ],
    [
      "-72692517740912320716/94381225",
      "243439239878556987280040254018/916913600875"
    ],
    [
      "-45559294273940010732/64368529",
      "211357141964018180299543516522/516428708167"
    ],
    [
      "-1696740463840671591/4631104",
      "6639874552796552656654966417/9966135808"
    ],
    [
      "60117603540459545/53824",
      "16567997157336097345086919/12487168"
    ],
    [
      "3860624772348929597/3254416",
      "8365827126584558806260415549/5870966464"
    ],
    [
      "414674289121711881532/419471361",
      "9959825390953634891163022949926/8591192944641"
    ],
    [
      "6343007061548220404149/3826659600",
      "522678548519204085226062556997573/236717162856000"
    ],
    [
      "-6646211405340703775/92006464",
      "603538051261638732746063413739/882526002688"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Source: Michael Rubinstein's elliptic-curves-by-rank collection, families/family_Z4.add_2026-10-24.part2.tsv.gz, 208066th data row, added on 24 October 2026:\r\nhttps://github.com/mrubinst/elliptic-curves-by-rank/blob/5e2e867ddb468765263bfadf520d9acda17a5a4b/families/family_Z4.add_2026-10-24.part2.tsv.gz\r\n\r\nThe source lists proven rank 9 and torsion Z/4. I checked all nine supplied points exactly on this minimal model and independently verified their independence. I checked the supplied torsion generator has exact order 4 and computed the full torsion group separately. Conductor 2121981965976696746916052177755. The source does not identify the construction method.",
  "created_at": "2026-10-25 21:48:42",
  "updated_at": "2026-10-25 21:48:42"
}