{
  "id": 2766,
  "curve_key": "688:-16640",
  "ainvs": [
    "0",
    "-1",
    "0",
    "-14",
    "24"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    2,
    2
  ],
  "naive_height": 19.60136651380003,
  "faltings_height": -0.40520681826668437,
  "conductor": "672",
  "bad_primes": [
    "2",
    "3",
    "7"
  ],
  "discriminant": "28224",
  "regulator": "0.9931091614598024517938796376206598194188",
  "points": [
    [
      "4",
      "4"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 672e1 = LMFDB 672.b3: https://www.lmfdb.org/EllipticCurve/Q/672/b/3\n\nMordell–Weil rank exactly 1 (Cremona's tables). Conductor 672, minimal discriminant 28224, torsion ℤ/2ℤ × ℤ/2ℤ. The witness is the generator from Cremona's tables.",
  "created_at": "2026-09-26 20:21:27",
  "updated_at": "2026-09-26 20:21:27"
}