{
  "id": 3585,
  "curve_key": "16781151287056:-68710076850118112704",
  "ainvs": [
    "0",
    "1",
    "0",
    "-349607318480",
    "79525435374086100"
  ],
  "rank_lower_bound": 4,
  "torsion": [
    4,
    2
  ],
  "naive_height": 91.3538322758544,
  "faltings_height": 5.360732551865813,
  "conductor": "114682154160",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "29",
    "37",
    "113",
    "563"
  ],
  "discriminant": "2671097302682984107634637519360000",
  "regulator": "211.3095341324471874534731725118502751552121978",
  "points": [
    [
      "138628",
      "183641514"
    ],
    [
      "328090",
      "11810400"
    ],
    [
      "332290",
      "6699000"
    ],
    [
      "1436610",
      "1594435080"
    ]
  ],
  "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)=(1998, 18270), with v-u=16272=113*12^2. PARI/GP gives exact rank 4 and torsion C2 x C4.",
  "created_at": "2026-09-28 21:46:10",
  "updated_at": "2026-09-28 21:46:10"
}