There are twelve long sword kata. You can find some interesting notes on the kata from Kampaibudokai here.
1 sassen (sashi sen)
2 hasso hidari
3 hasso migi
4 uke nagashi hidari
5 uke nagashi migi
6 moji gamae
7 haritsuke
8 nagashi uchi
9 tora bura
10 kazuki
11 aisen uchidome
12 amashi uchi
1 sassen (sashi sen)
2 hasso hidari
3 hasso migi
4 uke nagashi hidari
5 uke nagashi migi
6 moji gamae
7 haritsuke
8 nagashi uchi
9 tora bura
10 kazuki
11 aisen uchidome
12 amashi uchi