{
  "id": 1013,
  "curve_key": "1873:-45305",
  "ainvs": [
    "1",
    "1",
    "1",
    "-39",
    "36"
  ],
  "rank_lower_bound": 0,
  "torsion": [
    4,
    2
  ],
  "naive_height": 22.605890107332264,
  "faltings_height": -0.07035719017321967,
  "conductor": "231",
  "bad_primes": [
    "3",
    "7",
    "11"
  ],
  "discriminant": "2614689",
  "regulator": "1",
  "points": [],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 231a2 = LMFDB 231.a3: https://www.lmfdb.org/EllipticCurve/Q/231/a/3\n\nMordell–Weil rank exactly 0 (Cremona's tables). Conductor 231, minimal discriminant 2614689, torsion ℤ/2ℤ × ℤ/4ℤ.",
  "created_at": "2026-09-23 15:15:25",
  "updated_at": "2026-09-23 15:15:25"
}