You need to look into the startup locations in the registry. I don't remember what they are off the top of my head; google them.
If you can, download Process Hacker to see the parent process ID of the trojan (the program that opened it.) It may not be the "persistence" mechanism that actually opened it on startup, though.
Does this thing pop back up after you kill the process and delete the .exe? If so, you can run Process Monitor to try to see which process it re-creating the file.
Well if this "silly little trojan virus" is this sneaky that you can't get rid of it, who knows what other sneaky things it might be doing even if you happen to get rid of this .exe and the .exe that's re-creating it all the time...