{
  "id": 3270,
  "curve_key": "6067408:12122724160",
  "ainvs": [
    "0",
    "-1",
    "0",
    "-126404",
    "-13988796"
  ],
  "rank_lower_bound": 2,
  "torsion": [
    4,
    2
  ],
  "naive_height": 46.85532616114671,
  "faltings_height": 1.9103857215287896,
  "conductor": "50232",
  "bad_primes": [
    "2",
    "3",
    "7",
    "13",
    "23"
  ],
  "discriminant": "44213957363407104",
  "regulator": "6.79046028776988483926565546408697567992636",
  "points": [
    [
      "-176",
      "1666"
    ],
    [
      "494",
      "6624"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 50232r2 = LMFDB 50232.c5: https://www.lmfdb.org/EllipticCurve/Q/50232/c/5\n\nMordell–Weil rank exactly 2 (Cremona's tables). Conductor 50232, minimal discriminant 44213957363407104, torsion ℤ/2ℤ × ℤ/4ℤ. The witnesses are the generators from Cremona's tables.",
  "created_at": "2026-09-26 20:49:10",
  "updated_at": "2026-09-26 20:49:10"
}