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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_tag_links.object_type = 'P' 
  AND cscart_tags.status IN ('A') 
  AND cscart_tag_links.object_id = 1143 
GROUP BY 
  cscart_tags.tag_id 
ORDER BY 
  cscart_tags.tag asc

Query time 0.00046

Explain
id	select_type	table	type	possible_keys	key	key_len	ref	rows	Extra
1	SIMPLE	cscart_tag_links	ref	PRIMARY,tag_id,ids	PRIMARY	6	const,const	2	Using where; Using index; Using temporary; Using filesort
1	SIMPLE	cscart_tags	eq_ref	PRIMARY	PRIMARY	3	hobilifedt.cscart_tag_links.tag_id	1	Using where

Result

tag_id	object_id	object_type	tag	status	popularity
5	1143	P	17118615994	A	1
4	1143	P	17118617905	A	1