{
  "id": 5580,
  "curve_key": "11646148033:395341724560735",
  "ainvs": [
    "1",
    "1",
    "1",
    "-242628084",
    "-457672535499"
  ],
  "rank_lower_bound": 3,
  "torsion": [
    4,
    2
  ],
  "family": null,
  "families": [],
  "naive_height": 69.53472396402044,
  "faltings_height": 3.8564970738070605,
  "conductor": "11142978",
  "bad_primes": [
    "2",
    "3",
    "7",
    "11",
    "89",
    "271"
  ],
  "discriminant": "823671393846398572259119104",
  "regulator": "58.974823199516996317851139631800809642826048",
  "points": [
    [
      "-8745/4",
      "2006011/8"
    ],
    [
      "-2057",
      "181901"
    ],
    [
      "13336741/25",
      "48650990749/125"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Specialization at (u,v) = (271,352) of the C2 x C4 family y^2 = x(x+u^2)(x+v^2), giving y^2 = x(x+73441)(x+123904). Found in my own run scanning coprime positive integer pairs u < v, with 251 <= v <= 500 and conductor below 13086843. The displayed global minimal model [1,1,1,-242628084,-457672535499] is obtained by x = 4X - 65780, y = 8Y + 4X + 4. Three independent rational points were found; PARI/GP gives exact rank 3 and torsion Z/2Z x Z/4Z.",
  "created_at": "2026-10-23 19:16:24",
  "updated_at": "2026-10-23 19:16:24"
}