{
  "id": 3590,
  "curve_key": "3844194519568:-7077914551523165120",
  "ainvs": [
    "0",
    "-1",
    "0",
    "-80087385824",
    "8192057426724864"
  ],
  "rank_lower_bound": 4,
  "torsion": [
    4,
    2
  ],
  "naive_height": 86.93275562754565,
  "faltings_height": 5.193561269568425,
  "conductor": "42043148112",
  "bad_primes": [
    "2",
    "3",
    "7",
    "29",
    "103",
    "163",
    "257"
  ],
  "discriminant": "3884250278458477756167588826988544",
  "regulator": "5956.239403384666045032457882650102533004340774",
  "points": [
    [
      "-92228416/289",
      "173624418240/4913"
    ],
    [
      "23968016/25",
      "112681329264/125"
    ],
    [
      "3620380688/5929",
      "197402414891760/456533"
    ],
    [
      "45836593616/390625",
      "4944321215651664/244140625"
    ]
  ],
  "submitter": "Daniel Błażewicz",
  "history": [],
  "commentary": "(u,v) = (721,257) for the C2 x C4 family y^2 = x(x+u^2)(x+v^2). PARI/GP gives exact rank 4.",
  "created_at": "2026-09-29 04:49:16",
  "updated_at": "2026-09-29 04:49:16"
}