SELECT 
  category_id, 
  parent_id 
FROM 
  cscart_categories 
WHERE 
  parent_id IN(
    587, 581, 577, 565, 341, 555, 337, 537, 
    561, 345, 343, 334, 603
  )

Query time 0.00027

JSON explain

{
  "query_block": {
    "select_id": 1,
    "table": {
      "table_name": "cscart_categories",
      "access_type": "range",
      "possible_keys": ["parent"],
      "key": "parent",
      "key_length": "3",
      "used_key_parts": ["parent_id"],
      "rows": 13,
      "filtered": 100,
      "index_condition": "cscart_categories.parent_id in (587,581,577,565,341,555,337,537,561,345,343,334,603)"
    }
  }
}