{
  "id": 966,
  "curve_key": "25:611",
  "ainvs": [
    "1",
    "0",
    "1",
    "-1",
    "-1"
  ],
  "rank_lower_bound": 0,
  "torsion": [
    2
  ],
  "naive_height": 12.830193918343191,
  "faltings_height": -0.8739671385516418,
  "conductor": "69",
  "bad_primes": [
    "3",
    "23"
  ],
  "discriminant": "-207",
  "regulator": "1",
  "points": [],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 69a1 = LMFDB 69.a2: https://www.lmfdb.org/EllipticCurve/Q/69/a/2\n\nMordell–Weil rank exactly 0 (Cremona's tables). Conductor 69, minimal discriminant -207, torsion ℤ/2ℤ.",
  "created_at": "2026-09-23 15:07:53",
  "updated_at": "2026-09-23 15:07:53"
}