MySQL Performance: MySQL => troublesome "user's also took" query

I'm trying to optimize a query on the following table:

The user_quiz table looks like:

+---------------+----------+------+-----+---------+-------+
| Field         | Type     | Null | Key | Default | Extra |
+---------------+----------+------+-----+---------+-------+
| user_id       | int(12)  | NO   | PRI | NULL    |       |
| quiz_id       | int(12)  | NO   | PRI | NULL    |       |
| activity_date | datetime | NO   |     | NULL    |       |
+---------------+----------+------+-----+---------+-------+

The primary key is on user_id, quiz_id and there is an additional index on quiz_id.

The point of the query is to retrieve quizzes related to a particular quiz, sorted by how many users took both. The query looks like:

SELECT uquq.quiz_id
FROM   user_quiz uq, user_quiz uquq
WHERE  uq.quiz_id = ?
  AND  uq.user_id = uquq.user_id
GROUP BY uquq.quiz_id ORDER BY COUNT(*) DESC

The explain produces:

+----+-------------+-------+------+-----------------+---------+---------+-----------------+-------+----------------------------------------------+
| id | select_type | table | type | possible_keys   | key     | key_len | ref             | rows  | Extra                                        |
+----+-------------+-------+------+-----------------+---------+---------+-----------------+-------+----------------------------------------------+
|  1 | SIMPLE      | uq    | ref  | PRIMARY,quiz_id | quiz_id | 4       | const           | 14126 | Using index; Using temporary; Using filesort |
|  1 | SIMPLE      | uquq  | ref  | PRIMARY         | PRIMARY | 4       | quiz.uq.user_id |    13 | Using index                                  |
+----+-------------+-------+------+-----------------+---------+---------+-----------------+-------+----------------------------------------------+

This query seems to cause extreme load on our database server to the point where we've had to disable it.

I'd appreciate any insight you guys could offer, like how I might avoid the filesort. I have more info I could provide, but wasn't sure what might be applicable.