{
  "id": 2669,
  "curve_key": "-287:4751",
  "ainvs": [
    "1",
    "0",
    "0",
    "6",
    "-5"
  ],
  "rank_lower_bound": 3,
  "torsion": [],
  "naive_height": 16.978446647278865,
  "faltings_height": -0.46406821850460944,
  "conductor": "26743",
  "bad_primes": [
    "47",
    "569"
  ],
  "discriminant": "-26743",
  "regulator": "2.0829721641483903997939166220928417012294659",
  "points": [
    [
      "1",
      "1"
    ],
    [
      "2",
      "3"
    ],
    [
      "5",
      "10"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 26743a1 = LMFDB 26743.a1: https://www.lmfdb.org/EllipticCurve/Q/26743/a/1\n\nMordell–Weil rank exactly 3 (Cremona's tables). Conductor 26743, minimal discriminant -26743, torsion trivial. The witnesses are the generators from Cremona's tables.",
  "created_at": "2026-09-26 20:16:55",
  "updated_at": "2026-09-26 20:16:55"
}