{
  "id": 1032,
  "curve_key": "20161:-3140641",
  "ainvs": [
    "1",
    "0",
    "0",
    "-420",
    "3600"
  ],
  "rank_lower_bound": 0,
  "torsion": [
    8
  ],
  "naive_height": 29.91987495435613,
  "faltings_height": 0.4598698897925757,
  "conductor": "690",
  "bad_primes": [
    "2",
    "3",
    "5",
    "23"
  ],
  "discriminant": "-965779200",
  "regulator": "1",
  "points": [],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 690k1 = LMFDB 690.k5: https://www.lmfdb.org/EllipticCurve/Q/690/k/5\n\nMordell–Weil rank exactly 0 (Cremona's tables). Conductor 690, minimal discriminant -965779200, torsion ℤ/8ℤ.",
  "created_at": "2026-09-23 15:18:37",
  "updated_at": "2026-09-23 15:18:37"
}