{
  "id": 5907,
  "curve_key": "2263883066176:-3406126270186432000",
  "ainvs": [
    "0",
    "1",
    "0",
    "-47164230545",
    "3942260054268559"
  ],
  "rank_lower_bound": 9,
  "torsion": [
    2
  ],
  "family": null,
  "families": [],
  "naive_height": 85.3443078771602,
  "faltings_height": 4.784324682978587,
  "conductor": "74259467769292508224",
  "bad_primes": [
    "2",
    "17",
    "47",
    "89",
    "463",
    "1657",
    "14057"
  ],
  "discriminant": "625906662606597087417013256192",
  "regulator": "505749.91446918363993037159621018090924717615404479084525",
  "points": [
    [
      "113979",
      "6875072"
    ],
    [
      "122379",
      "-1785328"
    ],
    [
      "43669",
      "-44338732"
    ],
    [
      "1150489/9",
      "-38977192/27"
    ],
    [
      "124481",
      "-350304"
    ],
    [
      "63115",
      "-34884272"
    ],
    [
      "496461/4",
      "-5186989/8"
    ],
    [
      "129787",
      "-2681696"
    ],
    [
      "252019",
      "89792368"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Source: Michael Rubinstein's elliptic-curves-by-rank collection, rank_9.add_2026-10-24.tsv.gz, 1467th data row, added on 24 October 2026:\r\nhttps://github.com/mrubinst/elliptic-curves-by-rank/blob/5e2e867ddb468765263bfadf520d9acda17a5a4b/rank_9.add_2026-10-24.tsv.gz\r\n\r\nThe source lists proven rank 9 and torsion Z/2. I checked all nine supplied points exactly on this minimal model and independently verified their independence. The full torsion group was computed separately. Conductor 74259467769292508224. The source does not identify the construction method.",
  "created_at": "2026-10-25 21:05:22",
  "updated_at": "2026-10-25 21:05:22"
}