{
  "id": 932,
  "curve_key": "217:2755",
  "ainvs": [
    "1",
    "1",
    "0",
    "-4",
    "-5"
  ],
  "rank_lower_bound": 0,
  "torsion": [
    2,
    2
  ],
  "naive_height": 16.13969206062138,
  "faltings_height": -0.6649400524083601,
  "conductor": "39",
  "bad_primes": [
    "3",
    "13"
  ],
  "discriminant": "1521",
  "regulator": "1",
  "points": [],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 39a1 = LMFDB 39.a3: https://www.lmfdb.org/EllipticCurve/Q/39/a/3\n\nMordell–Weil rank exactly 0 (Cremona's tables). Conductor 39, minimal discriminant 1521, torsion ℤ/2ℤ × ℤ/2ℤ.",
  "created_at": "2026-09-23 15:02:32",
  "updated_at": "2026-09-23 15:02:32"
}