Actually the HMS Cyane in question was in built 1805 to replace the one built in 1796. Referring to 'displacement' is ridiculous as this type of measurement wasn't in use until many years later. She was 537 2/94 (two ninety-forths) tons 'builder's measurement'. The 1796 Cyane was an 18-gun ship sloop, of 420 tons.
(The Sailing Navy List, David Lyons, published by Conway, 1993 ISBN 0-85177-615-X)

The armament of Constitution varied slightly throughout her active career, but by the time of the 1812 War she usually carried 30 long 24 pounders and 20 to 24 32 pounder carronades.

It's a shame that these websites take their information from one source, without any checking, and then state their case so authoritively.