{
  "id": 2981,
  "curve_key": "913:-21689",
  "ainvs": [
    "1",
    "1",
    "1",
    "-19",
    "17"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    4
  ],
  "naive_height": 20.450207641784907,
  "faltings_height": -0.2838757677787535,
  "conductor": "438",
  "bad_primes": [
    "2",
    "3",
    "73"
  ],
  "discriminant": "168192",
  "regulator": "0.6653445420451020814164748484388166893316",
  "points": [
    [
      "5",
      "6"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 438f1 = LMFDB 438.e3: https://www.lmfdb.org/EllipticCurve/Q/438/e/3\n\nMordell–Weil rank exactly 1 (Cremona's tables). Conductor 438, minimal discriminant 168192, torsion ℤ/4ℤ. The witness is the generator from Cremona's tables.",
  "created_at": "2026-09-26 20:31:44",
  "updated_at": "2026-09-26 20:31:44"
}