{
  "id": 2628,
  "curve_key": "16264644835201:-63582403275639892801",
  "ainvs": [
    "1",
    "0",
    "0",
    "-338846767400",
    "73590716294760000"
  ],
  "rank_lower_bound": 2,
  "torsion": [
    6,
    2
  ],
  "naive_height": 91.2600445184297,
  "faltings_height": 5.521024064130014,
  "conductor": "329261790",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "13",
    "23",
    "47",
    "71"
  ],
  "discriminant": "150408294381649658861227708416000000",
  "regulator": "6.54955670822685879320993548727078239644690",
  "points": [
    [
      "-655280",
      "119736280"
    ],
    [
      "-578000",
      "276592600"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-47, q=8; A=(3q-p)(p+q)^3=-4211649, B=-(p+3q)(p-q)^3=-3826625. The listed points are independent modulo torsion by the exact 2-descent Kummer squareclass map. The rank is a proven lower bound; no upper bound is claimed.",
  "created_at": "2026-09-26 20:13:41",
  "updated_at": "2026-09-26 20:13:41"
}