{
  "id": 915,
  "curve_key": "48:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "-1",
    "0"
  ],
  "rank_lower_bound": 0,
  "torsion": [
    2,
    2
  ],
  "naive_height": 11.613603032723672,
  "faltings_height": -0.9639593356315369,
  "conductor": "32",
  "bad_primes": [
    "2"
  ],
  "discriminant": "64",
  "regulator": "1",
  "points": [],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 32a2 = LMFDB 32.a3: https://www.lmfdb.org/EllipticCurve/Q/32/a/3\n\nMordell–Weil rank exactly 0 (Cremona's tables). Conductor 32, minimal discriminant 64, torsion ℤ/2ℤ × ℤ/2ℤ.",
  "created_at": "2026-09-23 15:00:22",
  "updated_at": "2026-09-23 15:00:22"
}