{
  "id": 935,
  "curve_key": "193:-5921",
  "ainvs": [
    "1",
    "1",
    "1",
    "-4",
    "5"
  ],
  "rank_lower_bound": 0,
  "torsion": [
    8
  ],
  "naive_height": 17.37252126506355,
  "faltings_height": -0.5040459871422248,
  "conductor": "42",
  "bad_primes": [
    "2",
    "3",
    "7"
  ],
  "discriminant": "-16128",
  "regulator": "1",
  "points": [],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 42a1 = LMFDB 42.a5: https://www.lmfdb.org/EllipticCurve/Q/42/a/5\n\nMordell–Weil rank exactly 0 (Cremona's tables). Conductor 42, minimal discriminant -16128, torsion ℤ/8ℤ.",
  "created_at": "2026-09-23 15:02:33",
  "updated_at": "2026-09-23 15:02:33"
}