{
  "id": 3311,
  "curve_key": "11188816:-37426282136",
  "ainvs": [
    "0",
    "-1",
    "1",
    "-233100",
    "43395156"
  ],
  "rank_lower_bound": 2,
  "torsion": [
    5
  ],
  "naive_height": 48.69127805095248,
  "faltings_height": 1.6294833417939798,
  "conductor": "199595",
  "bad_primes": [
    "5",
    "11",
    "19",
    "191"
  ],
  "discriminant": "-1826418996875",
  "regulator": "7.24194430913651360628349414528870041204051",
  "points": [
    [
      "300",
      "612"
    ],
    [
      "277",
      "60"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 199595a1 = LMFDB 199595.b1: https://www.lmfdb.org/EllipticCurve/Q/199595/b/1\n\nMordell–Weil rank exactly 2 (Cremona's tables). Conductor 199595, minimal discriminant -1826418996875, torsion ℤ/5ℤ. The witnesses are the generators from Cremona's tables.",
  "created_at": "2026-09-26 20:55:48",
  "updated_at": "2026-09-26 20:55:48"
}