{
  "id": 2776,
  "curve_key": "3504:-62208",
  "ainvs": [
    "0",
    "0",
    "0",
    "-73",
    "72"
  ],
  "rank_lower_bound": 2,
  "torsion": [
    2,
    2
  ],
  "naive_height": 24.484981356168845,
  "faltings_height": 0.10295073127373855,
  "conductor": "19040",
  "bad_primes": [
    "2",
    "5",
    "7",
    "17"
  ],
  "discriminant": "22657600",
  "regulator": "3.48392505938217146539182355580682639094515",
  "points": [
    [
      "-1",
      "12"
    ],
    [
      "9",
      "12"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 19040h1 = LMFDB 19040.b3: https://www.lmfdb.org/EllipticCurve/Q/19040/b/3\n\nMordell–Weil rank exactly 2 (Cremona's tables). Conductor 19040, minimal discriminant 22657600, torsion ℤ/2ℤ × ℤ/2ℤ. The witnesses are the generators from Cremona's tables.",
  "created_at": "2026-09-26 20:21:56",
  "updated_at": "2026-09-26 20:21:56"
}