{
  "id": 2126,
  "curve_key": "1585:-65449",
  "ainvs": [
    "1",
    "0",
    "0",
    "-33",
    "73"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    3
  ],
  "naive_height": 22.17805298476503,
  "faltings_height": -0.22890242379382578,
  "conductor": "682",
  "bad_primes": [
    "2",
    "11",
    "31"
  ],
  "discriminant": "-174592",
  "regulator": "0.7167725770394235363084694923629693385188",
  "points": [
    [
      "-6",
      "11"
    ]
  ],
  "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 = 20-5/2.",
  "created_at": "2026-09-26 10:37:00",
  "updated_at": "2026-09-26 10:37:00"
}