{
  "id": 2827,
  "curve_key": "10993:115255",
  "ainvs": [
    "1",
    "1",
    "1",
    "-229",
    "-229"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    4,
    2
  ],
  "naive_height": 27.91504195673659,
  "faltings_height": 0.3938836823164157,
  "conductor": "1254",
  "bad_primes": [
    "2",
    "3",
    "11",
    "19"
  ],
  "discriminant": "761097744",
  "regulator": "2.249900062403558931989000744229923137178",
  "points": [
    [
      "-3",
      "22"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 1254h2 = LMFDB 1254.g4: https://www.lmfdb.org/EllipticCurve/Q/1254/g/4\n\nMordell–Weil rank exactly 1 (Cremona's tables). Conductor 1254, minimal discriminant 761097744, torsion ℤ/2ℤ × ℤ/4ℤ. The witness is the generator from Cremona's tables.",
  "created_at": "2026-09-26 20:24:13",
  "updated_at": "2026-09-26 20:24:13"
}