{
  "id": 3276,
  "curve_key": "1153:-56161",
  "ainvs": [
    "1",
    "0",
    "0",
    "-24",
    "63"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    4
  ],
  "naive_height": 21.871955689617938,
  "faltings_height": -0.15205154165303048,
  "conductor": "429",
  "bad_primes": [
    "3",
    "11",
    "13"
  ],
  "discriminant": "-938223",
  "regulator": "1.057726598219751847551203229976946544026",
  "points": [
    [
      "6",
      "9"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 429b1 = LMFDB 429.b5: https://www.lmfdb.org/EllipticCurve/Q/429/b/5\n\nMordell–Weil rank exactly 1 (Cremona's tables). Conductor 429, minimal discriminant -938223, torsion ℤ/4ℤ. The witness is the generator from Cremona's tables.",
  "created_at": "2026-09-26 20:50:08",
  "updated_at": "2026-09-26 20:50:08"
}