{
  "id": 2134,
  "curve_key": "21024:-3048408",
  "ainvs": [
    "0",
    "0",
    "1",
    "-438",
    "3528"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    3
  ],
  "naive_height": 29.860260090196345,
  "faltings_height": 0.015108444383325518,
  "conductor": "1755",
  "bad_primes": [
    "3",
    "5",
    "13"
  ],
  "discriminant": "-1755",
  "regulator": "5.623494497965827781666690826022352607858",
  "points": [
    [
      "-158/9",
      "2044/27"
    ]
  ],
  "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 = -12/1.",
  "created_at": "2026-09-26 10:41:52",
  "updated_at": "2026-09-26 10:41:52"
}