Am chord inversions
Am/C and Am/E are the first and second inversions of the A minor. This means that the bass tone is shifting from A to C or E.
Try in chord progressions
Am - Am/C - C
Am/E - Em - G
When stumble upon these chord names, you can choose to ignore the alternate bass note and just play the regular A minor. It will always sound ok, but it may lack some subtle harmonic additions.
A fingering for Am/C in closed position is XXX555.
Theory of the Am/C and Am/E chords
Both chords consist of the notes A, C, E. The difference is that the order of notes shifts. C is the bass note in the first inversion and E is the bass note in the second inversion.
Alternative chord names
Am/C is identical with C6(no5).
See also Am7 inversions
Chord constructionAm x - A - E - A - C - E
Am/C x - C - E - A - C - E
Am/E E - A - E - A - C - E
Guitar versions of the chord
Notes in chordAm A - C - E
Am/C C - E - A
Am/E E - A - C
Only the order of notes differs