While in captivity, Hiccup and Camicazi are allowed to keep their swords in order to practice for a gladiatorial event during Saturn's Day Saturday. When they arrive in the arena on The Valhalla Express (as the stadium has been intentionally flooded), Camicazi waves the Invincible at the crowd as she can understand that they are making fun of her even though she does not speak Latin.
No written description is given in How to Speak Dragonese of the Invincible. Camicazi is, however, depicted throughout the book with a sword in hand, presumably the same sword. It does not appear to be particularly ornate, and appears to nearly be as long as Camicazi's legs.
The Invincible is presumably the sword which Camicazi wields in all subsequent books, though it is not specifically named.