{
  "id": 933,
  "curve_key": "336:5184",
  "ainvs": [
    "0",
    "0",
    "0",
    "-7",
    "-6"
  ],
  "rank_lower_bound": 0,
  "torsion": [
    2,
    2
  ],
  "naive_height": 17.451333479889612,
  "faltings_height": -0.5487873722761626,
  "conductor": "40",
  "bad_primes": [
    "2",
    "5"
  ],
  "discriminant": "6400",
  "regulator": "1",
  "points": [],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 40a1 = LMFDB 40.a2: https://www.lmfdb.org/EllipticCurve/Q/40/a/2\n\nMordell–Weil rank exactly 0 (Cremona's tables). Conductor 40, minimal discriminant 6400, torsion ℤ/2ℤ × ℤ/2ℤ.",
  "created_at": "2026-09-23 15:02:32",
  "updated_at": "2026-09-23 15:02:32"
}