{
  "id": 908,
  "curve_key": "1440:-54648",
  "ainvs": [
    "0",
    "0",
    "1",
    "-30",
    "63"
  ],
  "rank_lower_bound": 0,
  "torsion": [
    3
  ],
  "naive_height": 21.81733579282337,
  "faltings_height": -0.49715821192695564,
  "conductor": "27",
  "bad_primes": [
    "3"
  ],
  "discriminant": "-243",
  "regulator": "1",
  "points": [],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 27a4 = LMFDB 27.a2: https://www.lmfdb.org/EllipticCurve/Q/27/a/2\n\nMordell–Weil rank exactly 0 (Cremona's tables). Conductor 27, minimal discriminant -243, torsion ℤ/3ℤ.",
  "created_at": "2026-09-23 14:59:18",
  "updated_at": "2026-09-23 14:59:18"
}