{
  "id": 3591,
  "curve_key": "2660765406736:-4336770728068807616",
  "ainvs": [
    "0",
    "-1",
    "0",
    "-55432612640",
    "5019429042432000"
  ],
  "rank_lower_bound": 4,
  "torsion": [
    4,
    2
  ],
  "naive_height": 85.82890483267258,
  "faltings_height": 4.917319107118817,
  "conductor": "3415094160",
  "bad_primes": [
    "2",
    "3",
    "5",
    "79",
    "281",
    "641"
  ],
  "discriminant": "17226541308161684144876945817600",
  "regulator": "1506.602476006220968652739918688435003612409282",
  "points": [
    [
      "100805",
      "21351330"
    ],
    [
      "2421296/25",
      "2955837456/125"
    ],
    [
      "6862384/49",
      "594933200/343"
    ],
    [
      "462461616/1225",
      "8346531448464/42875"
    ]
  ],
  "submitter": "Daniel Błażewicz",
  "history": [],
  "commentary": "(u,v) = (641,79) 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 05:52:08",
  "updated_at": "2026-09-29 05:52:08"
}