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SELECT 
  cscart_tags.tag_id, 
  cscart_tag_links.object_id, 
  cscart_tag_links.object_type, 
  cscart_tags.tag, 
  cscart_tags.status, 
  COUNT(cscart_tag_links.tag_id) as popularity 
FROM 
  cscart_tags 
  LEFT JOIN cscart_tag_links ON cscart_tag_links.tag_id = cscart_tags.tag_id 
WHERE 
  1 
  AND cscart_tags.company_id = 2 
  AND cscart_tag_links.object_type = 'A' 
  AND cscart_tags.status IN ('A') 
  AND cscart_tag_links.object_id = 51 
GROUP BY 
  cscart_tags.tag_id 
ORDER BY 
  cscart_tags.tag asc

Query time 0.00034

JSON explain

{
  "query_block": {
    "select_id": 1,
    "table": {
      "table_name": "cscart_tags",
      "access_type": "system",
      "possible_keys": ["PRIMARY"],
      "rows": 1,
      "filtered": 100
    },
    "table": {
      "table_name": "cscart_tag_links",
      "access_type": "system",
      "possible_keys": ["PRIMARY", "tag_id", "ids"],
      "rows": 1,
      "filtered": 100
    }
  }
}

Result

tag_id	object_id	object_type	tag	status	popularity
1	51	A	新着情報	A	1