{
  "id": 1190,
  "curve_key": "1588315065900481:-62581065940653223785121",
  "ainvs": [
    "1",
    "0",
    "0",
    "-33089897206260",
    "72431786525672019600"
  ],
  "rank_lower_bound": 2,
  "torsion": [
    8,
    2
  ],
  "naive_height": 105.00435042682669,
  "faltings_height": 6.621112654079805,
  "conductor": "169350090",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "13",
    "17",
    "41",
    "89"
  ],
  "discriminant": "52386387326982250326891111127449600000000",
  "regulator": "16.1451419529730691095098975188826762911041",
  "points": [
    [
      "2202120",
      "3199316940"
    ],
    [
      "-12574970/9",
      "290739959030/27"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Found by a rational-parameter search of y^2=x(x+u^4)(x+v^4), with u=m^2-n^2 and v=2mn, at (m,n)=(8,5). Converted to the global minimal model; PARI/GP ellrank returned bounds [2,2]. The 2 supplied points and the torsion subgroup are independently certified by the site.",
  "created_at": "2026-09-23 21:40:13",
  "updated_at": "2026-09-23 21:40:13"
}