{
  "id": 3569,
  "curve_key": "49057761805456:-340744476254044071104",
  "ainvs": [
    "0",
    "-1",
    "0",
    "-1022036704280",
    "394380521528489472"
  ],
  "rank_lower_bound": 4,
  "torsion": [
    4,
    2
  ],
  "naive_height": 94.57205859642504,
  "faltings_height": 5.738297061073174,
  "conductor": "449224966320",
  "bad_primes": [
    "2",
    "3",
    "5",
    "13",
    "19",
    "29",
    "43",
    "59",
    "103"
  ],
  "discriminant": "1133536362512549414586614670188160000",
  "regulator": "292.1028173662118931812687939939870432449073681",
  "points": [
    [
      "438734",
      "174438810"
    ],
    [
      "4074574",
      "7992290150"
    ],
    [
      "8763752",
      "25778342304"
    ],
    [
      "534924896/529",
      "7645621978800/12167"
    ]
  ],
  "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)=(1180,5356), with v-u=4176=29*12^2. PARI/GP gives exact rank 4 and torsion C2 x C4.\r\n",
  "created_at": "2026-09-28 19:10:29",
  "updated_at": "2026-09-28 19:10:29"
}