{
  "id": 2199,
  "curve_key": "5609652596187201:-419724832679971011720801",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-116867762420567",
    "485792659633573720559"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    6,
    2
  ],
  "naive_height": 108.78979556014342,
  "faltings_height": 6.8396432434079015,
  "conductor": "1193061870",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "17",
    "19",
    "41"
  ],
  "discriminant": "206450972407865730924482032247782464000000",
  "regulator": "1.905135106379449815709589644954579555140",
  "points": [
    [
      "6480267",
      "764712766"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-33, q=52; A=(3q-p)(p+q)^3=1296351, B=-(p+3q)(p-q)^3=75537375. 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 19:46:36",
  "updated_at": "2026-09-26 19:46:36"
}