{
  "id": 5933,
  "curve_key": "2775321568:-515224457105536",
  "ainvs": [
    "0",
    "1",
    "0",
    "-57819199",
    "596305330065"
  ],
  "rank_lower_bound": 8,
  "torsion": [
    2
  ],
  "family": null,
  "families": [],
  "naive_height": 67.75124752136382,
  "faltings_height": 3.701121868694682,
  "conductor": "498435640849536128",
  "bad_primes": [
    "2",
    "73",
    "89",
    "97",
    "113",
    "193",
    "311",
    "911"
  ],
  "discriminant": "-141249755289390209201682688",
  "regulator": "98871.9974133849403519934348105944597506177202961956977",
  "points": [
    [
      "6512",
      "704257"
    ],
    [
      "-608",
      "794503"
    ],
    [
      "23689",
      "-3538462"
    ],
    [
      "9449",
      "945358"
    ],
    [
      "-7191",
      "-800178"
    ],
    [
      "11144",
      "1155877"
    ],
    [
      "467536/25",
      "307613459/125"
    ],
    [
      "27935",
      "4558660"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Source: Michael Rubinstein's elliptic-curves-by-rank collection, torsion/torsion_Z2.add_2026-10-24.part3.tsv.gz, 484245th data row, added on 24 October 2026:\r\nhttps://github.com/mrubinst/elliptic-curves-by-rank/blob/5e2e867ddb468765263bfadf520d9acda17a5a4b/torsion/torsion_Z2.add_2026-10-24.part3.tsv.gz\r\n\r\nThe source lists proven rank 8 and torsion Z/2. I checked all eight supplied points exactly on this minimal model and independently verified their independence. The full torsion group and supplied torsion generator were checked separately. Conductor 498435640849536128. The source does not identify the construction method.",
  "created_at": "2026-10-25 22:31:28",
  "updated_at": "2026-10-25 22:31:28"
}