{
  "id": 2217,
  "curve_key": "2292265678731889:-109636819068395571099913",
  "ainvs": [
    "1",
    "0",
    "0",
    "-47755534973581",
    "126894462534718811345"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    6,
    2
  ],
  "naive_height": 106.1049513081677,
  "faltings_height": 6.616048695157269,
  "conductor": "2534390430",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "13",
    "17",
    "19",
    "31",
    "59"
  ],
  "discriminant": "14141504328586429962859627450137444993600",
  "regulator": "5.611157348389398489196669899942878883701",
  "points": [
    [
      "4161728",
      "477466121"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-55, q=38; A=(3q-p)(p+q)^3=-830297, B=-(p+3q)(p-q)^3=47457063. 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 19:47:44",
  "updated_at": "2026-09-26 19:47:44"
}