{
  "id": 2715,
  "curve_key": "329473:-193587841",
  "ainvs": [
    "1",
    "0",
    "0",
    "-6864",
    "223488"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    8
  ],
  "naive_height": 38.16248385216477,
  "faltings_height": 1.0826161263311054,
  "conductor": "1974",
  "bad_primes": [
    "2",
    "3",
    "7",
    "47"
  ],
  "discriminant": "-990247845888",
  "regulator": "1.235275546924371023389779629162531398048",
  "points": [
    [
      "54",
      "78"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 1974i1 = LMFDB 1974.h5: https://www.lmfdb.org/EllipticCurve/Q/1974/h/5\n\nMordell–Weil rank exactly 1 (Cremona's tables). Conductor 1974, minimal discriminant -990247845888, torsion ℤ/8ℤ. The witness is the generator from Cremona's tables.",
  "created_at": "2026-09-26 20:19:01",
  "updated_at": "2026-09-26 20:19:01"
}