{
  "id": 2907,
  "curve_key": "169:2123",
  "ainvs": [
    "1",
    "0",
    "1",
    "-4",
    "-3"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    2
  ],
  "naive_height": 15.38969614476922,
  "faltings_height": -0.797070468815284,
  "conductor": "185",
  "bad_primes": [
    "5",
    "37"
  ],
  "discriminant": "185",
  "regulator": "1.425265290672122006906800183092672845772",
  "points": [
    [
      "3",
      "2"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 185c1 = LMFDB 185.c1: https://www.lmfdb.org/EllipticCurve/Q/185/c/1\n\nMordell–Weil rank exactly 1 (Cremona's tables). Conductor 185, minimal discriminant 185, torsion ℤ/2ℤ. The witness is the generator from Cremona's tables.",
  "created_at": "2026-09-26 20:27:49",
  "updated_at": "2026-09-26 20:27:49"
}