{
  "id": 2133,
  "curve_key": "14905:-1819693",
  "ainvs": [
    "1",
    "0",
    "1",
    "-311",
    "2080"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    3
  ],
  "naive_height": 28.828356727012007,
  "faltings_height": -0.05325973597501724,
  "conductor": "1358",
  "bad_primes": [
    "2",
    "7",
    "97"
  ],
  "discriminant": "-1358",
  "regulator": "5.378365919528966679714283252311279390127",
  "points": [
    [
      "-11/16",
      "3055/64"
    ]
  ],
  "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 = -11/1.",
  "created_at": "2026-09-26 10:40:23",
  "updated_at": "2026-09-26 10:40:23"
}