{
  "id": 2129,
  "curve_key": "6345:-505413",
  "ainvs": [
    "1",
    "-1",
    "0",
    "-132",
    "618"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    3
  ],
  "naive_height": 26.266267140445464,
  "faltings_height": -0.22070531011054498,
  "conductor": "702",
  "bad_primes": [
    "2",
    "3",
    "13"
  ],
  "discriminant": "702",
  "regulator": "3.365198176839262188210969104763162797608",
  "points": [
    [
      "7/4",
      "151/8"
    ]
  ],
  "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 = 45+9/1.",
  "created_at": "2026-09-26 10:38:40",
  "updated_at": "2026-09-26 10:38:40"
}