{
  "id": 2429,
  "curve_key": "264159732711169:-4293385889610468212353",
  "ainvs": [
    "1",
    "0",
    "0",
    "-5503327764816",
    "4969196172882950400"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    6,
    2
  ],
  "naive_height": 99.6227252527662,
  "faltings_height": 5.698198581417282,
  "conductor": "10748010",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "13",
    "31",
    "127"
  ],
  "discriminant": "4396435535331793706632504934400",
  "regulator": "4.322980429480206310529624649049299933216",
  "points": [
    [
      "1342248",
      "23819496"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-31, q=32; A=(3q-p)(p+q)^3=127, B=-(p+3q)(p-q)^3=16253055. 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 20:01:03",
  "updated_at": "2026-09-26 20:01:03"
}