{
  "id": 2936,
  "curve_key": "4233:257499",
  "ainvs": [
    "1",
    "-1",
    "0",
    "-88",
    "-276"
  ],
  "rank_lower_bound": 3,
  "torsion": [
    2
  ],
  "naive_height": 25.05199872156277,
  "faltings_height": 0.04003426903965405,
  "conductor": "162418",
  "bad_primes": [
    "2",
    "17",
    "281"
  ],
  "discriminant": "5522212",
  "regulator": "6.8267305833990556842818380793931336674775554",
  "points": [
    [
      "-6",
      "6"
    ],
    [
      "-5",
      "7"
    ],
    [
      "-25/4",
      "31/8"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 162418c1 = LMFDB 162418.b1: https://www.lmfdb.org/EllipticCurve/Q/162418/b/1\n\nMordell–Weil rank exactly 3 (Cremona's tables). Conductor 162418, minimal discriminant 5522212, torsion ℤ/2ℤ. The witnesses are the generators from Cremona's tables.",
  "created_at": "2026-09-26 20:29:08",
  "updated_at": "2026-09-26 20:29:08"
}