{
  "id": 2849,
  "curve_key": "2083201:-2950964801",
  "ainvs": [
    "1",
    "1",
    "1",
    "-43400",
    "3397385"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    8
  ],
  "naive_height": 43.64824863308098,
  "faltings_height": 1.5300399957724462,
  "conductor": "18690",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "89"
  ],
  "discriminant": "192320100000000",
  "regulator": "1.532262183558395160655384273741095404155",
  "points": [
    [
      "135",
      "79"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 18690m1 = LMFDB 18690.l5: https://www.lmfdb.org/EllipticCurve/Q/18690/l/5\n\nMordell–Weil rank exactly 1 (Cremona's tables). Conductor 18690, minimal discriminant 192320100000000, torsion ℤ/8ℤ. The witness is the generator from Cremona's tables.",
  "created_at": "2026-09-26 20:25:12",
  "updated_at": "2026-09-26 20:25:12"
}