{
  "id": 2984,
  "curve_key": "673:-27665",
  "ainvs": [
    "1",
    "1",
    "1",
    "-14",
    "26"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    4
  ],
  "naive_height": 20.45584671066442,
  "faltings_height": -0.261635036166498,
  "conductor": "777",
  "bad_primes": [
    "3",
    "7",
    "37"
  ],
  "discriminant": "-266511",
  "regulator": "1.748805510252616867776149934880211141245",
  "points": [
    [
      "4",
      "5"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 777d1 = LMFDB 777.c4: https://www.lmfdb.org/EllipticCurve/Q/777/c/4\n\nMordell–Weil rank exactly 1 (Cremona's tables). Conductor 777, minimal discriminant -266511, torsion ℤ/4ℤ. The witness is the generator from Cremona's tables.",
  "created_at": "2026-09-26 20:31:53",
  "updated_at": "2026-09-26 20:31:53"
}