{
  "id": 905,
  "curve_key": "129:-2241",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-3",
    "3"
  ],
  "rank_lower_bound": 0,
  "torsion": [
    7
  ],
  "naive_height": 15.429354947601855,
  "faltings_height": -0.6831605484242721,
  "conductor": "26",
  "bad_primes": [
    "2",
    "13"
  ],
  "discriminant": "-1664",
  "regulator": "1",
  "points": [],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 26b1 = LMFDB 26.b2: https://www.lmfdb.org/EllipticCurve/Q/26/b/2\n\nMordell–Weil rank exactly 0 (Cremona's tables). Conductor 26, minimal discriminant -1664, torsion ℤ/7ℤ.",
  "created_at": "2026-09-23 14:58:15",
  "updated_at": "2026-09-23 14:58:15"
}