{
  "id": 2128,
  "curve_key": "1057:-32689",
  "ainvs": [
    "1",
    "0",
    "0",
    "-22",
    "36"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    3
  ],
  "naive_height": 20.889569957610714,
  "faltings_height": -0.3209468842500202,
  "conductor": "254",
  "bad_primes": [
    "2",
    "127"
  ],
  "discriminant": "65024",
  "regulator": "0.4313428242716647493693851746510562336053",
  "points": [
    [
      "-4",
      "10"
    ]
  ],
  "submitter": "hdeping",
  "history": [],
  "commentary": "Specialization of the torsion Z/3 family E: y^2+a*x*y+b^3*y=x^3, arising from x/y+y/z+z/x = k with k = 35+7/2.",
  "created_at": "2026-09-26 10:38:05",
  "updated_at": "2026-09-26 10:38:05"
}