Many English verbs can be spelt with either -ise or -ize. In American English, -ize is preferred in these cases. Examples:
mechanize/mechanise (GB) mechanize (US) computerize/computerise (GB) computerize (US)
Words of two syllables usually have -ise in both British and American English.
surprise (NOT surprize) revise advise comprise despise (but GB and US capsize, baptize; GB also baptise)
A number of longer words only have -ise, in both British and American English. These include:
compromise exercise improvise supervise televise advertise (US also advertize)
Note also analyse (US analyze).
If in doubt, use -iseó it is almost always correct, at least in British English.