Context is important here as well. I would the open E if the next chord were an F variant or something the low E will lead in to.

In these days, Google is a handy tool. For your reading pleasure:

[fender.com]

If it's marked with an "X" - don't play that string.
If it's marked with an "O" - play it open.
If there's NO mark, it's optional. Obviously, playing the open E in the Am/E chord would be correct, but not mandatory.

You must listen to what you are playing, it need not agree with any chord chart, as notation goes it’s little more than a jumping off point. If you like what you played do it even if it’s wrong... follow the music grasshopper.

yep pretty much agree with ken. Youd have to play the low E to make it sound like its label of course (and thats the third inversion btw, second inversion would have a C as the bass note). to me, x means to mute the string, an o would mean to play it open, but the absence of the x or o sorta means don't mute it but don't lay into it so hard either id kinda let it ring with the chord but not make it the focal point if that makes any sense.

Copy link: [dai.ly]

It's music. There's often not a right or wrong. Play both and see how much difference you think it makes to the tune/song. I don't really use chords much but i would take the x in the diagram to mean don't play this string and nothing above the diagram would make it kind of optional.
Chords, especially, on the guitar are often not an exact science. Music is about sound so your ears are often the most reliable indicators

Yeah, what kenriley said.