{
  "id": 2769,
  "curve_key": "784:-9152",
  "ainvs": [
    "0",
    "-1",
    "0",
    "-16",
    "16"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    2,
    2
  ],
  "naive_height": 19.993227061051222,
  "faltings_height": -0.27717050546999455,
  "conductor": "240",
  "bad_primes": [
    "2",
    "3",
    "5"
  ],
  "discriminant": "230400",
  "regulator": "0.4458105698536916058150170973611500783877",
  "points": [
    [
      "0",
      "4"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 240c2 = LMFDB 240.a3: https://www.lmfdb.org/EllipticCurve/Q/240/a/3\n\nMordell–Weil rank exactly 1 (Cremona's tables). Conductor 240, minimal discriminant 230400, torsion ℤ/2ℤ × ℤ/2ℤ. The witness is the generator from Cremona's tables.",
  "created_at": "2026-09-26 20:21:37",
  "updated_at": "2026-09-26 20:21:37"
}