{
  "id": 949,
  "curve_key": "-39:-189",
  "ainvs": [
    "1",
    "-1",
    "0",
    "1",
    "0"
  ],
  "rank_lower_bound": 0,
  "torsion": [
    2
  ],
  "naive_height": 10.99068493838894,
  "faltings_height": -0.9788126605347042,
  "conductor": "55",
  "bad_primes": [
    "5",
    "11"
  ],
  "discriminant": "-55",
  "regulator": "1",
  "points": [],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 55a4 = LMFDB 55.a4: https://www.lmfdb.org/EllipticCurve/Q/55/a/4\n\nMordell–Weil rank exactly 0 (Cremona's tables). Conductor 55, minimal discriminant -55, torsion ℤ/2ℤ.",
  "created_at": "2026-09-23 15:04:41",
  "updated_at": "2026-09-23 15:04:41"
}