{
  "id": 3079,
  "curve_key": "-368:4456",
  "ainvs": [
    "0",
    "-1",
    "1",
    "8",
    "-8"
  ],
  "rank_lower_bound": 3,
  "torsion": [],
  "naive_height": 17.724248814506794,
  "faltings_height": -0.42841980971059984,
  "conductor": "40331",
  "bad_primes": [
    "31",
    "1301"
  ],
  "discriminant": "-40331",
  "regulator": "2.0808883681314856576060184124397381944582699",
  "points": [
    [
      "1",
      "0"
    ],
    [
      "2",
      "3"
    ],
    [
      "4",
      "8"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 40331c1 = LMFDB 40331.a1: https://www.lmfdb.org/EllipticCurve/Q/40331/a/1\n\nMordell–Weil rank exactly 3 (Cremona's tables). Conductor 40331, minimal discriminant -40331, torsion trivial. The witnesses are the generators from Cremona's tables.",
  "created_at": "2026-09-26 20:36:15",
  "updated_at": "2026-09-26 20:36:15"
}