The humble A minor triad is often the first minor chord that a piano student would learn. It's the relative minor of C major which means that the key of A minor shares the same key signature as the key of C major. Below is a list of some modified Am chords and possible ways to voice them.
Look at the Am7 above. It resembles a C major triad with an A in the bass, ie. C/A. The next chord along Am7add11 looks like a C2/A. You won't see these chords written as C/A or C2/A because these symbols don't convey the true minor quality of the chord, but from a piano improvisation angle, it's quite handy to think of the Am chord as a C over A.
In fact, I encourage all beginner students to pair these two chords in their heads. When you see an Am chord symbol, think "C". This is because any basic modification (eg. C2, Cmaj7) or any cool run that can be applied to a C chord, can be converted into an equally cool Am chord or run, by playing an A in the bass instead of a C. This principle makes it very easy to produce some great sounding Am chords with minimal effort.
Here are more variations of the Am piano chord. These modifications result in a harsher effect and are often played in jazz. The final chord Adim7 isn't technically an Am chord variant as it's based on the diminished triad and not the minor one, but it does sound sufficiently "sad" and complex so I just added it to the mix!
Watch the video and get a feel for the differing qualities of each chord, then experiment with them in your own playing. Invert them, or modify them further. Build your own collection of Am chord piano voicings, and the next time you see an Am on a lead sheet, you'll have a dozen options to choose from!