I only include these rare, and sometimes unique, trumpets for the sake of completeness. There have been several instruments called a Contrabass Trumpet over the years. Some of these are pitched in F below the regular Bass Trumpet, while others are a full octave lower than the Bass Trumpet. The instrument in F is the equivalent of an Bass Tuba, while the one in C or B-flat is the same pitch as the Contrabass Tuba.
These instruments have never been made by any manufacturer. Their existence is due to adventurous instrument repairmen experimenting with creating new instruments for bored tuba players to try (these instruments are always played by tubists). Like many other odd instruments, it is best not to write for the Contrabass Trumpet in your scoring.
The 2nd instrument (after the B-flat Cornet) is a Contrabass Trumpet in F. The final instrument is a Contrabass instrument in B-flat, but I hesitate to call that a trumpet. Due to its bore, it is in the tuba family.
However, there is a viable alternative to the Contrabass Trumpet: the Cimbasso. The Cimbasso is an Italian valved Bass/Contrabass Trombone pitched either in F or B-flat. The presence of valves on the Cimbasso essentially makes this a Contrabass Trumpet. They are much used in the works of Verdi, Puccini, and by modern Hollywood composers.
F Cimbasso playing excerpts from Verdi.
Amassed Cimbassi (F and B-flat) and Bass Trumpets playing Finlandia.