{
  "id": 5899,
  "curve_key": "6906156386464:-18148742241785387648",
  "ainvs": [
    "0",
    "-1",
    "0",
    "-143878258051",
    "21005536665189475"
  ],
  "rank_lower_bound": 9,
  "torsion": [
    2
  ],
  "family": null,
  "families": [],
  "naive_height": 88.6903030789607,
  "faltings_height": 5.03644770939723,
  "conductor": "637009094394841111680",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "19",
    "23",
    "31",
    "53",
    "83",
    "313",
    "887",
    "1823"
  ],
  "discriminant": "7092885343457274325136947188480",
  "regulator": "3597572.4770564657321026876538486928728389986103497485199",
  "points": [
    [
      "1835226",
      "2436820507"
    ],
    [
      "-352374",
      "-167185507"
    ],
    [
      "1686394/9",
      "674920961/27"
    ],
    [
      "595269/4",
      "-430050419/8"
    ],
    [
      "-59406",
      "171298327"
    ],
    [
      "302301/4",
      "822233159/8"
    ],
    [
      "7578469/36",
      "1469500883/216"
    ],
    [
      "9473101/36",
      "-7983133937/216"
    ],
    [
      "235386",
      "-13434443"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Source: Michael Rubinstein's elliptic-curves-by-rank collection, rank_9.add_2026-10-24.tsv.gz, 2024th 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 637009094394841111680. The source does not identify the construction method.",
  "created_at": "2026-10-25 20:31:57",
  "updated_at": "2026-10-25 20:31:57"
}