SELECT 
  category_id, 
  parent_id 
FROM 
  q_categories 
WHERE 
  parent_id IN(
    3, 10, 11, 138, 144, 245, 405, 432, 578, 
    589, 617
  )

Query time 0.00046

JSON explain

{
  "query_block": {
    "select_id": 1,
    "cost_info": {
      "query_cost": "78.21"
    },
    "table": {
      "table_name": "q_categories",
      "access_type": "range",
      "possible_keys": [
        "parent"
      ],
      "key": "parent",
      "used_key_parts": [
        "parent_id"
      ],
      "key_length": "3",
      "rows_examined_per_scan": 48,
      "rows_produced_per_join": 48,
      "filtered": "100.00",
      "index_condition": "(`portal`.`q_categories`.`parent_id` in (3,10,11,138,144,245,405,432,578,589,617))",
      "cost_info": {
        "read_cost": "68.61",
        "eval_cost": "9.60",
        "prefix_cost": "78.21",
        "data_read_per_join": "126K"
      },
      "used_columns": [
        "category_id",
        "parent_id"
      ]
    }
  }
}