{
  "id": 950,
  "curve_key": "-48:-1728",
  "ainvs": [
    "0",
    "0",
    "0",
    "1",
    "2"
  ],
  "rank_lower_bound": 0,
  "torsion": [
    4
  ],
  "naive_height": 14.909439898728001,
  "faltings_height": -0.6951800073585328,
  "conductor": "56",
  "bad_primes": [
    "2",
    "7"
  ],
  "discriminant": "-1792",
  "regulator": "1",
  "points": [],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 56a1 = LMFDB 56.a4: https://www.lmfdb.org/EllipticCurve/Q/56/a/4\n\nMordell–Weil rank exactly 0 (Cremona's tables). Conductor 56, minimal discriminant -1792, torsion ℤ/4ℤ.",
  "created_at": "2026-09-23 15:05:43",
  "updated_at": "2026-09-23 15:05:43"
}