{
  "id": 2747,
  "curve_key": "145:487",
  "ainvs": [
    "1",
    "1",
    "1",
    "-3",
    "-2"
  ],
  "rank_lower_bound": 2,
  "torsion": [],
  "naive_height": 14.930201227261723,
  "faltings_height": -0.6924804500242822,
  "conductor": "1627",
  "bad_primes": [
    "1627"
  ],
  "discriminant": "1627",
  "regulator": "0.479877399706461244321122652383092454328435",
  "points": [
    [
      "-1",
      "1"
    ],
    [
      "-2",
      "1"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 1627a1 = LMFDB 1627.a1: https://www.lmfdb.org/EllipticCurve/Q/1627/a/1\n\nMordell–Weil rank exactly 2 (Cremona's tables). Conductor 1627, minimal discriminant 1627, torsion trivial. The witnesses are the generators from Cremona's tables.",
  "created_at": "2026-09-26 20:20:29",
  "updated_at": "2026-09-26 20:20:29"
}