SELECT 
  category_id, 
  parent_id 
FROM 
  cscart_categories 
WHERE 
  parent_id IN(1045, 3134, 3708)

Query time 0.00023

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": 20,
      "filtered": 100,
      "index_condition": "cscart_categories.parent_id in (1045,3134,3708)"
    }
  }
}

Result

category_id parent_id
1046 1045
1047 1045
1048 1045
1049 1045
1050 1045
1051 1045
1052 1045
1053 1045
1054 1045
2367 1045
2366 1045
2415 1045
3135 3134
3136 3134
3137 3134
3138 3134
3139 3134
3140 3134
3141 3134
3142 3134
3143 3134