It is terminal 5 at London Heathrow Airport.

Terminal 5 at London Heathrow Airport opened to the public on Thursday March 27th, 2008.

Yes, there are three stations: Heathrow Terminal's 1,2 &3; Heathrow Terminal 4 and Heathrow Terminal 5. They are all situated on the Piccadilly Line.

London Underground's (Tube) Picadilly Line goes to Heathrow Terminal 5.

This is the cheapest AND the slowest way to get to Heathrow. However, the Heathrow Express train, which costs £32 for return ticket, will get you comfortably within 20 minutes from Terminal 5 to the Paddington Station in the centere of London.

see also these links for more info:

Transport for London- http://www.tfl.gov.uk/

British Airways- http://www.terminal5.ba.com/en/to-and-from-terminal-5/london-underground/

Note: Only half of the Heathrow branch Piccadilly trains go to Terminal 5, so you will have to change at either Hatton Cross or Terminal 1,2,3 station if you aren't on this train

London Underground serves Heathrow Airport from three different stations: Heathrow Terminals 1,2,3; Heathrow Terminal 4 and Heathrow Terminal 5. These stations are all on the Piccadilly line which runs through Central London. However, the travel-card does not cover you to travel on Heathrow Express which I believe is what you are referring to.