{
  "id": 3061,
  "curve_key": "87144976:-813507212224",
  "ainvs": [
    "0",
    "1",
    "0",
    "-1815520",
    "940954100"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    8
  ],
  "naive_height": 54.849251041604454,
  "faltings_height": 2.1798870574730818,
  "conductor": "4080",
  "bad_primes": [
    "2",
    "3",
    "5",
    "17"
  ],
  "discriminant": "3746786595840000",
  "regulator": "2.787974465583163158996294034088007291876",
  "points": [
    [
      "610",
      "7800"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 4080be7 = LMFDB 4080.ba1: https://www.lmfdb.org/EllipticCurve/Q/4080/ba/1\n\nMordell–Weil rank exactly 1 (Cremona's tables). Conductor 4080, minimal discriminant 3746786595840000, torsion ℤ/8ℤ. The witness is the generator from Cremona's tables.",
  "created_at": "2026-09-26 20:35:27",
  "updated_at": "2026-09-26 20:35:27"
}