{
  "id": 3583,
  "curve_key": "32677127429776:-186704337399572240576",
  "ainvs": [
    "0",
    "-1",
    "0",
    "-680773488120",
    "216093210025852800"
  ],
  "rank_lower_bound": 4,
  "torsion": [
    4,
    2
  ],
  "naive_height": 93.35308944633381,
  "faltings_height": 5.527207084679637,
  "conductor": "446214180720",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "19",
    "89",
    "109",
    "131"
  ],
  "discriminant": "19648422355159062563798332534809600",
  "regulator": "414.7477977540629712075522245910702687978318286",
  "points": [
    [
      "673692",
      "251442972"
    ],
    [
      "1234296",
      "1120825200"
    ],
    [
      "2030727470/3721",
      "19136745071950/226981"
    ],
    [
      "5658927864/10609",
      "75155217009840/1092727"
    ]
  ],
  "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)=(1572, 14388), with v-u=12816=89*12^2. PARI/GP gives exact rank 4 and torsion C2 x C4.",
  "created_at": "2026-09-28 21:29:18",
  "updated_at": "2026-09-28 21:29:18"
}