{
  "id": 3068,
  "curve_key": "-47:1799",
  "ainvs": [
    "1",
    "0",
    "0",
    "1",
    "-2"
  ],
  "rank_lower_bound": 2,
  "torsion": [],
  "naive_height": 14.989972467901067,
  "faltings_height": -0.6890032611389955,
  "conductor": "1933",
  "bad_primes": [
    "1933"
  ],
  "discriminant": "-1933",
  "regulator": "0.755018996646126740980464274379304186894051",
  "points": [
    [
      "1",
      "0"
    ],
    [
      "2",
      "2"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 1933a1 = LMFDB 1933.a1: https://www.lmfdb.org/EllipticCurve/Q/1933/a/1\n\nMordell–Weil rank exactly 2 (Cremona's tables). Conductor 1933, minimal discriminant -1933, torsion trivial. The witnesses are the generators from Cremona's tables.",
  "created_at": "2026-09-26 20:35:46",
  "updated_at": "2026-09-26 20:35:46"
}