{
  "id": 2806,
  "curve_key": "553:-11861",
  "ainvs": [
    "1",
    "1",
    "0",
    "-11",
    "9"
  ],
  "rank_lower_bound": 2,
  "torsion": [
    2
  ],
  "naive_height": 18.946074004567006,
  "faltings_height": -0.4537856208934023,
  "conductor": "2742",
  "bad_primes": [
    "2",
    "3",
    "457"
  ],
  "discriminant": "16452",
  "regulator": "0.611034784270383171759655271923023151497548",
  "points": [
    [
      "0",
      "3"
    ],
    [
      "1",
      "0"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 2742c1 = LMFDB 2742.a2: https://www.lmfdb.org/EllipticCurve/Q/2742/a/2\n\nMordell–Weil rank exactly 2 (Cremona's tables). Conductor 2742, minimal discriminant 16452, torsion ℤ/2ℤ. The witnesses are the generators from Cremona's tables.",
  "created_at": "2026-09-26 20:23:16",
  "updated_at": "2026-09-26 20:23:16"
}