{
  "id": 969,
  "curve_key": "-80:-3160",
  "ainvs": [
    "0",
    "1",
    "1",
    "2",
    "4"
  ],
  "rank_lower_bound": 0,
  "torsion": [
    5
  ],
  "naive_height": 16.116654613161916,
  "faltings_height": -0.5930983340946728,
  "conductor": "75",
  "bad_primes": [
    "3",
    "5"
  ],
  "discriminant": "-6075",
  "regulator": "1",
  "points": [],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 75c1 = LMFDB 75.a2: https://www.lmfdb.org/EllipticCurve/Q/75/a/2\n\nMordell–Weil rank exactly 0 (Cremona's tables). Conductor 75, minimal discriminant -6075, torsion ℤ/5ℤ.",
  "created_at": "2026-09-23 15:07:55",
  "updated_at": "2026-09-23 15:07:55"
}