{
  "id": 3283,
  "curve_key": "76921:-21333581",
  "ainvs": [
    "1",
    "1",
    "0",
    "-1602",
    "24024"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    4
  ],
  "naive_height": 33.75160260041469,
  "faltings_height": 0.43599339611509375,
  "conductor": "330",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11"
  ],
  "discriminant": "4392300",
  "regulator": "0.5216761379606932399799023420757016726328",
  "points": [
    [
      "23",
      "-9"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 330e3 = LMFDB 330.b1: https://www.lmfdb.org/EllipticCurve/Q/330/b/1\n\nMordell–Weil rank exactly 1 (Cremona's tables). Conductor 330, minimal discriminant 4392300, torsion ℤ/4ℤ. The witness is the generator from Cremona's tables.",
  "created_at": "2026-09-26 20:51:16",
  "updated_at": "2026-09-26 20:51:16"
}