{
  "id": 3571,
  "curve_key": "450087077169808:-9515392701628545241280",
  "ainvs": [
    "0",
    "-1",
    "0",
    "-9376814107704",
    "11013189122859963264"
  ],
  "rank_lower_bound": 4,
  "torsion": [
    4,
    2
  ],
  "naive_height": 101.2213865543852,
  "faltings_height": 6.25634797931569,
  "conductor": "3333579476304",
  "bad_primes": [
    "2",
    "3",
    "7",
    "11",
    "53",
    "59",
    "211",
    "1367"
  ],
  "discriminant": "367599161688691688170524025270242223104",
  "regulator": "6382.872269341372424546570728959478715993348411",
  "points": [
    [
      "-2781389211/841",
      "58991603910246/24389"
    ],
    [
      "11794264113/1024",
      "1239555396004695/32768"
    ],
    [
      "16389655781/8836",
      "38749954968725/830584"
    ],
    [
      "46744593996/22801",
      "2194328392183620/3442951"
    ]
  ],
  "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)=(1652,9284), with v-u=7632=53*12^2. PARI/GP gives exact rank 4 and torsion C2 x C4.",
  "created_at": "2026-09-28 19:21:40",
  "updated_at": "2026-09-28 19:21:40"
}