{
  "id": 3284,
  "curve_key": "329473:-189116641",
  "ainvs": [
    "1",
    "0",
    "0",
    "-6864",
    "218313"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    4
  ],
  "naive_height": 38.115749061691105,
  "faltings_height": 0.5410956389069148,
  "conductor": "429",
  "bad_primes": [
    "3",
    "11",
    "13"
  ],
  "discriminant": "1287",
  "regulator": "4.230906392879007390204812919907786176104",
  "points": [
    [
      "104",
      "743"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 429b4 = LMFDB 429.b1: https://www.lmfdb.org/EllipticCurve/Q/429/b/1\n\nMordell–Weil rank exactly 1 (Cremona's tables). Conductor 429, minimal discriminant 1287, torsion ℤ/4ℤ. The witness is the generator from Cremona's tables.",
  "created_at": "2026-09-26 20:51:26",
  "updated_at": "2026-09-26 20:51:26"
}