{
  "id": 994,
  "curve_key": "-32:-440",
  "ainvs": [
    "0",
    "-1",
    "1",
    "1",
    "0"
  ],
  "rank_lower_bound": 1,
  "torsion": [],
  "naive_height": 12.173549453824613,
  "faltings_height": -0.9110458683316546,
  "conductor": "131",
  "bad_primes": [
    "131"
  ],
  "discriminant": "-131",
  "regulator": "0.2160951986677483660829254961619972058465",
  "points": [
    [
      "0",
      "0"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 131a1 = LMFDB 131.a1: https://www.lmfdb.org/EllipticCurve/Q/131/a/1\n\nMordell–Weil rank exactly 1 (Cremona's tables). Conductor 131, minimal discriminant -131, trivial torsion. The witness is the generator from Cremona's tables.",
  "created_at": "2026-09-23 15:12:12",
  "updated_at": "2026-09-23 15:12:12"
}