{
  "id": 2227,
  "curve_key": "3211820725899769:-181995010064147276211853",
  "ainvs": [
    "1",
    "0",
    "1",
    "-66912931789579",
    "210642367183352068706"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    6,
    2
  ],
  "naive_height": 107.11684312674954,
  "faltings_height": 6.636019742606368,
  "conductor": "233395890",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "13",
    "17",
    "47",
    "107"
  ],
  "discriminant": "5956057222412798076478078846113521122500",
  "regulator": "7.261252017459820525355376540043125266918",
  "points": [
    [
      "5085853",
      "1369757198"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-34, q=47; A=(3q-p)(p+q)^3=384475, B=-(p+3q)(p-q)^3=56864187. 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 19:48:21",
  "updated_at": "2026-09-26 19:48:21"
}