{
  "id": 3380,
  "curve_key": "13582625252946561:164120166462743201258559",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-282971359436387",
    "-189953825626075883101"
  ],
  "rank_lower_bound": 3,
  "torsion": [
    6,
    2
  ],
  "naive_height": 111.44270344785981,
  "faltings_height": 7.35447615388091,
  "conductor": "11232328230",
  "bad_primes": [
    "2",
    "3",
    "5",
    "17",
    "19",
    "67",
    "73",
    "79"
  ],
  "discriminant": "1434543971556124814588210417337986527296000000",
  "regulator": "140.38933961339788042562465605188991682148680",
  "points": [
    [
      "17292219",
      "9349614802"
    ],
    [
      "1176557307",
      "40352354309746"
    ],
    [
      "61189873467/3481",
      "3357199906792334/205379"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Found in a rational-parameter search of the Kubert–Tate family for torsion ℤ/2ℤ × ℤ/6ℤ: y^2 + (1-c)xy - by = x^3 - bx^2 with c=(10-2t)/(t^2-9), b=c+c^2, at t = -183/85; converted to the global minimal model. The 3 witness points were found with PARI/GP ellrank. Conductor 11232328230, torsion ℤ/2ℤ × ℤ/6ℤ.",
  "created_at": "2026-09-26 21:17:44",
  "updated_at": "2026-09-26 21:17:44"
}