{
  "id": 3199,
  "curve_key": "1936:-84160",
  "ainvs": [
    "0",
    "1",
    "0",
    "-40",
    "84"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    2
  ],
  "naive_height": 22.705137803509565,
  "faltings_height": -0.23466883556014265,
  "conductor": "112",
  "bad_primes": [
    "2",
    "7"
  ],
  "discriminant": "100352",
  "regulator": "0.1199599493626012880058198856226613030411",
  "points": [
    [
      "2",
      "4"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 112a2 = LMFDB 112.a1: https://www.lmfdb.org/EllipticCurve/Q/112/a/1\n\nMordell–Weil rank exactly 1 (Cremona's tables). Conductor 112, minimal discriminant 100352, torsion ℤ/2ℤ. The witness is the generator from Cremona's tables.",
  "created_at": "2026-09-26 20:42:16",
  "updated_at": "2026-09-26 20:42:16"
}