{
  "id": 959,
  "curve_key": "-48:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "1",
    "0"
  ],
  "rank_lower_bound": 0,
  "torsion": [
    2
  ],
  "naive_height": 11.613603032723672,
  "faltings_height": -0.9639593356315369,
  "conductor": "64",
  "bad_primes": [
    "2"
  ],
  "discriminant": "-64",
  "regulator": "1",
  "points": [],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 64a4 = LMFDB 64.a4: https://www.lmfdb.org/EllipticCurve/Q/64/a/4\n\nMordell–Weil rank exactly 0 (Cremona's tables). Conductor 64, minimal discriminant -64, torsion ℤ/2ℤ.",
  "created_at": "2026-09-23 15:06:49",
  "updated_at": "2026-09-23 15:06:49"
}