{
  "id": 5897,
  "curve_key": "3759268086976:-7287874364791521280",
  "ainvs": [
    "0",
    "1",
    "0",
    "-78318085145",
    "8435013668035879"
  ],
  "rank_lower_bound": 9,
  "torsion": [
    2
  ],
  "family": null,
  "families": [],
  "naive_height": 86.8657361899888,
  "faltings_height": 4.941355251359695,
  "conductor": "29064479945762992576",
  "bad_primes": [
    "2",
    "23",
    "41",
    "73",
    "113",
    "353",
    "1697",
    "2377"
  ],
  "discriminant": "7654400796689968404371928584192",
  "regulator": "237040.31210621284938403478396414971491115837309832245117",
  "points": [
    [
      "152647",
      "-6071264"
    ],
    [
      "1742743/9",
      "621753848/27"
    ],
    [
      "43489",
      "71493292"
    ],
    [
      "542497",
      "354410036"
    ],
    [
      "164722",
      "-1945961"
    ],
    [
      "921951",
      "848459144"
    ],
    [
      "206421",
      "32620256"
    ],
    [
      "165642",
      "-2653579"
    ],
    [
      "317511",
      "124810144"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Source: Michael Rubinstein's elliptic-curves-by-rank collection, rank_9.add_2026-10-24.tsv.gz, 1023rd data row, added 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 29064479945762992576. The source does not identify the construction method.",
  "created_at": "2026-10-25 20:27:12",
  "updated_at": "2026-10-25 20:27:12"
}