{
  "id": 2743,
  "curve_key": "-80:-1432",
  "ainvs": [
    "0",
    "1",
    "1",
    "2",
    "2"
  ],
  "rank_lower_bound": 2,
  "torsion": [],
  "naive_height": 14.533654695041182,
  "faltings_height": -0.7080758470250906,
  "conductor": "1483",
  "bad_primes": [
    "1483"
  ],
  "discriminant": "-1483",
  "regulator": "0.395288186152922788838107840821414308901883",
  "points": [
    [
      "-1",
      "0"
    ],
    [
      "0",
      "1"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 1483a1 = LMFDB 1483.a1: https://www.lmfdb.org/EllipticCurve/Q/1483/a/1\n\nMordell–Weil rank exactly 2 (Cremona's tables). Conductor 1483, minimal discriminant -1483, torsion trivial. The witnesses are the generators from Cremona's tables.",
  "created_at": "2026-09-26 20:20:19",
  "updated_at": "2026-09-26 20:20:19"
}