I see we can fetch tags via the api, which works fine, using https://api.stackexchange.com/2.2/badges?order=desc&sort=rank&site=stackoverflow but sadly, there doesn't seem to be a way to get the count number of all possible tags.
currently http://stackoverflow.com/tags shows 36 tags per page with pagination up to page 1426, which means there are around ~51336 tags.
Does the API have any such feature?