{
  "id": 977,
  "curve_key": "369:-8073",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-8",
    "11"
  ],
  "rank_lower_bound": 0,
  "torsion": [
    6
  ],
  "naive_height": 17.99256087879003,
  "faltings_height": -0.5183617207093277,
  "conductor": "90",
  "bad_primes": [
    "2",
    "3",
    "5"
  ],
  "discriminant": "-8640",
  "regulator": "1",
  "points": [],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 90b1 = LMFDB 90.b3: https://www.lmfdb.org/EllipticCurve/Q/90/b/3\n\nMordell–Weil rank exactly 0 (Cremona's tables). Conductor 90, minimal discriminant -8640, torsion ℤ/6ℤ.",
  "created_at": "2026-09-23 15:09:00",
  "updated_at": "2026-09-23 15:09:00"
}