{
  "id": 2729,
  "curve_key": "-458667999:-23159717283249",
  "ainvs": [
    "1",
    "-1",
    "1",
    "9555583",
    "26802839441"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    9
  ],
  "naive_height": 61.546871122890465,
  "faltings_height": 3.2042656747708445,
  "conductor": "417690",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "13",
    "17"
  ],
  "discriminant": "-366241548885849000000000",
  "regulator": "2.144954042440379449187235777052255795846",
  "points": [
    [
      "4681",
      "414894"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 417690cy2 = LMFDB 417690.cy3: https://www.lmfdb.org/EllipticCurve/Q/417690/cy/3\n\nMordell–Weil rank exactly 1 (Cremona's tables). Conductor 417690, minimal discriminant -366241548885849000000000, torsion ℤ/9ℤ. The witness is the generator from Cremona's tables.",
  "created_at": "2026-09-26 20:19:40",
  "updated_at": "2026-09-26 20:19:40"
}