{
  "id": 2996,
  "curve_key": "-6719:-1584449",
  "ainvs": [
    "1",
    "1",
    "1",
    "140",
    "1892"
  ],
  "rank_lower_bound": 2,
  "torsion": [
    4
  ],
  "naive_height": 28.551494541570772,
  "faltings_height": 0.44967017718484786,
  "conductor": "33915",
  "bad_primes": [
    "3",
    "5",
    "7",
    "17",
    "19"
  ],
  "discriminant": "-1628360895",
  "regulator": "8.81538981697858622529877633059865072305185",
  "points": [
    [
      "0",
      "43"
    ],
    [
      "16",
      "84"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 33915g1 = LMFDB 33915.d4: https://www.lmfdb.org/EllipticCurve/Q/33915/d/4\n\nMordell–Weil rank exactly 2 (Cremona's tables). Conductor 33915, minimal discriminant -1628360895, torsion ℤ/4ℤ. The witnesses are the generators from Cremona's tables.",
  "created_at": "2026-09-26 20:32:33",
  "updated_at": "2026-09-26 20:32:33"
}