{
  "id": 21,
  "curve_key": "40906085584:-8217699530925248",
  "ainvs": [
    "0",
    "-1",
    "0",
    "-852210116",
    "9511510378980"
  ],
  "rank_lower_bound": 6,
  "naive_height": 73.30363404213483,
  "faltings_height": 3.9568488879557058,
  "conductor": "5131476003533880",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "17",
    "19",
    "23",
    "29",
    "2179"
  ],
  "discriminant": "531185208959529592186118400",
  "regulator": "37742.286448328310471088273953984925467953157552812",
  "points": [
    [
      "-10234",
      "4142592"
    ],
    [
      "15153",
      "277620"
    ],
    [
      "-8324",
      "4003558"
    ],
    [
      "54376",
      "11133058"
    ],
    [
      "-128603/4",
      "15339115/8"
    ],
    [
      "-177656/9",
      "116575766/27"
    ]
  ],
  "submitter": "David Renshaw",
  "commentary": "Found by Penney - Pomerance (1974). A curve of rank exactly 6, via Dujella's elliptic-curve rank-records tables.",
  "created_at": "2026-05-27 22:12:03",
  "updated_at": "2026-07-01 23:00:15"
}