{
  "id": 2960,
  "curve_key": "28816:172864",
  "ainvs": [
    "0",
    "-1",
    "0",
    "-600",
    "0"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    4,
    2
  ],
  "naive_height": 30.80605820224721,
  "faltings_height": 0.6353360244244795,
  "conductor": "1680",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7"
  ],
  "discriminant": "13829760000",
  "regulator": "1.242447211373483671912572321217854360667",
  "points": [
    [
      "30",
      "90"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 1680d4 = LMFDB 1680.h3: https://www.lmfdb.org/EllipticCurve/Q/1680/h/3\n\nMordell–Weil rank exactly 1 (Cremona's tables). Conductor 1680, minimal discriminant 13829760000, torsion ℤ/2ℤ × ℤ/4ℤ. The witness is the generator from Cremona's tables.",
  "created_at": "2026-09-26 20:30:16",
  "updated_at": "2026-09-26 20:30:16"
}