{
  "id": 3586,
  "curve_key": "1468554573328:-1433249507624500160",
  "ainvs": [
    "0",
    "-1",
    "0",
    "-30594886944",
    "1658863795083264"
  ],
  "rank_lower_bound": 4,
  "torsion": [
    4,
    2
  ],
  "naive_height": 84.04589924858566,
  "faltings_height": 5.0111044627622725,
  "conductor": "6762560016",
  "bad_primes": [
    "2",
    "3",
    "17",
    "53",
    "271",
    "577"
  ],
  "discriminant": "644072796305919355861812317405184",
  "regulator": "1803.562934026105955288637949107393402806376495",
  "points": [
    [
      "135728",
      "2579920"
    ],
    [
      "-647139/25",
      "6166294434/125"
    ],
    [
      "7969109/49",
      "10763594570/343"
    ],
    [
      "32845077424/2025",
      "5952237498007568/91125"
    ]
  ],
  "submitter": "Daniel Błażewicz",
  "history": [],
  "commentary": "Inspired by (much better) curve#3566\r\nSpecialized curve of the C2 x C4 family y^2 = x(x+u^2)(x+v^2), where u±v=d*w^2. Here (u,v)=(2168, 4616), with v-u=2448=17*12^2. PARI/GP gives exact rank 4 and torsion C2 x C4.",
  "created_at": "2026-09-28 21:55:43",
  "updated_at": "2026-09-28 21:55:43"
}