{
  "id": 894,
  "curve_key": "2353:113975",
  "ainvs": [
    "1",
    "0",
    "0",
    "-49",
    "-136"
  ],
  "rank_lower_bound": 0,
  "torsion": [
    2,
    2
  ],
  "naive_height": 23.290339166182086,
  "faltings_height": -0.2723682068890329,
  "conductor": "21",
  "bad_primes": [
    "3",
    "7"
  ],
  "discriminant": "21609",
  "regulator": "1",
  "points": [],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 21a2 = LMFDB 21.a2: https://www.lmfdb.org/EllipticCurve/Q/21/a/2\n\nMordell–Weil rank exactly 0 (Cremona's tables). Conductor 21, minimal discriminant 21609, torsion ℤ/2ℤ × ℤ/2ℤ.",
  "created_at": "2026-09-23 14:56:06",
  "updated_at": "2026-09-23 14:56:06"
}