{
  "id": 3065,
  "curve_key": "-143:919",
  "ainvs": [
    "1",
    "1",
    "1",
    "3",
    "0"
  ],
  "rank_lower_bound": 2,
  "torsion": [],
  "naive_height": 14.888533890779723,
  "faltings_height": -0.67115578378897,
  "conductor": "2181",
  "bad_primes": [
    "3",
    "727"
  ],
  "discriminant": "-2181",
  "regulator": "0.745548011675010499223838574638368248393567",
  "points": [
    [
      "0",
      "0"
    ],
    [
      "2",
      "3"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 2181a1 = LMFDB 2181.a1: https://www.lmfdb.org/EllipticCurve/Q/2181/a/1\n\nMordell–Weil rank exactly 2 (Cremona's tables). Conductor 2181, minimal discriminant -2181, torsion trivial. The witnesses are the generators from Cremona's tables.",
  "created_at": "2026-09-26 20:35:37",
  "updated_at": "2026-09-26 20:35:37"
}