{
  "id": 3352,
  "curve_key": "2904048:-1594719360",
  "ainvs": [
    "0",
    "0",
    "0",
    "-60501",
    "1845740"
  ],
  "rank_lower_bound": 4,
  "torsion": [
    2,
    2
  ],
  "naive_height": 44.644848551147525,
  "faltings_height": 1.782012801040983,
  "conductor": "50089248",
  "bad_primes": [
    "2",
    "3",
    "11",
    "97",
    "163"
  ],
  "discriminant": "12701472123852864",
  "regulator": "63.28248322148087395477429128767029427244138278",
  "points": [
    [
      "-163",
      "2716"
    ],
    [
      "-97",
      "2608"
    ],
    [
      "904",
      "26190"
    ],
    [
      "-167/4",
      "16587/8"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Found in a Mestre–Nagao-sieved search of the family y^2 = x(x+a)(x+b), at a = 198, b = 489; converted to the global minimal model. The 4 witness points were found with PARI/GP ellrank. Conductor 50089248, torsion ℤ/2ℤ × ℤ/2ℤ.",
  "created_at": "2026-09-26 21:10:35",
  "updated_at": "2026-09-26 21:10:35"
}