{
  "id": 3246,
  "curve_key": "432:-7776",
  "ainvs": [
    "0",
    "0",
    "0",
    "-9",
    "9"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    3
  ],
  "naive_height": 18.205276764732332,
  "faltings_height": -0.49435290170064444,
  "conductor": "324",
  "bad_primes": [
    "2",
    "3"
  ],
  "discriminant": "11664",
  "regulator": "0.3876245949042761905184396586176523590703",
  "points": [
    [
      "1",
      "1"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 324c1 = LMFDB 324.a2: https://www.lmfdb.org/EllipticCurve/Q/324/a/2\n\nMordell–Weil rank exactly 1 (Cremona's tables). Conductor 324, minimal discriminant 11664, torsion ℤ/3ℤ. The witness is the generator from Cremona's tables.",
  "created_at": "2026-09-26 20:45:15",
  "updated_at": "2026-09-26 20:45:15"
}