Trains 77 & 78 are the Gumarang, Eksekutif, Bisnis & Ekonomi class, air-conditioned. Prices vary, with cheaper fares if you pre-book, for example Eksekutif class from Rp 250,000.
Trains 143 & 144 are the Jayabaya, Ekonomi class only, air-conditioned. Prices vary by date & train, check fares at tiket.id or How to buy tickets: At the station, at Indomaret minimarkets or online at as shown here.
Trains 51 & 52 are the Taksaka Pagi, Eksekutif class only, air-conditioned. Approaching Cirebon you'll see the vast shadow of Mt Cereme in the distance to the south, its summit usually hidden by cloud.
Trains 117 & 118 are the Fajar Utama, Bisnis class only, air-conditioned. It's an active volcano and the highest point in west Java.
Both cities should feature on any sensible trip to Java. You can check train times & fares using English) or tiket.id (in Indonesian).
It's easy to travel from Jakarta to Yogya or Solo by comfortable air-conditioned train, indeed it's the best way. Train 7 & 8 is the Argo Lawu, Eksekutif class only, air-conditioned.
Trains 1, 2, 3 & 4 are the Argo Bromo Anggrek (the Bromo Orchid), Eksekutif class only, air-conditioned.
It has comfortable reclining seats with footrests and a catering car.
There is both a daytime service and a time-effective overnight service, although the night trains have no sleepers - these disappeared from Indonesian trains in the 1990s.
Bookings are computerised and can be made up to 90 days in advance.
Indonesian trains run on narrow-gauge 3' 6" tracks, but are pretty fast and usually very punctual.