Thanks to all! Muting, of course, is a second nature. If I finger, my right hand thumb rests on the lower strings. Still this E-string manages to resonate audibly. Picking is a lot worse, as much of the muting is then being done with the other hand.
A piece of foam near the bridge does reduce it, but makes it sound dull.
I also tried to de-tune the E slightly. This reduces the ringing a lot. Unfortunately this de-tuning can be heared.
For writer "Over the Moon", playing a flagiolet (also written as flageolet) is done by deviding a string in harmonically mutually resonating parts, by just touching it with a finger. So if you touch a sting in the middle (fret 12) and play it, you will hear a note at twice the frequency of the open string. Once sounding, the finger can be removed from the string. This is also a great way to quickly check the tuning and intonation of your instrument.