{
  "id": 940,
  "curve_key": "1168:-38080",
  "ainvs": [
    "0",
    "1",
    "0",
    "-24",
    "36"
  ],
  "rank_lower_bound": 0,
  "torsion": [
    4,
    2
  ],
  "naive_height": 21.189144490164516,
  "faltings_height": -0.29877869579988464,
  "conductor": "48",
  "bad_primes": [
    "2",
    "3"
  ],
  "discriminant": "82944",
  "regulator": "1",
  "points": [],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 48a3 = LMFDB 48.a3: https://www.lmfdb.org/EllipticCurve/Q/48/a/3\n\nMordell–Weil rank exactly 0 (Cremona's tables). Conductor 48, minimal discriminant 82944, torsion ℤ/2ℤ × ℤ/4ℤ.",
  "created_at": "2026-09-23 15:03:37",
  "updated_at": "2026-09-23 15:03:37"
}