The standard grips this chord is usually shown with.
Eb13 is Eb, G, Bb, Db, F and C, a dominant thirteenth. The shape this page opens on is written x65688, lowest string first.
Note by note. Eb is the root, G is the major third, Bb is the fifth, Db is the flat seventh, F is the ninth and C is the thirteenth.

Also written Ebdom13 or Eb dominant 13. The same chord either way; which spelling you meet depends on who wrote the chart.
There are 8 common shapes for Eb13 on the guitar, and 47 derived voicings in 4 families.
One note away. Change a single note of Eb13 and you have Ebmaj13 (with one note moved), Eb69 (with one note taken away), Eb9 (with one note taken away) or Eb9#11 (with one note moved).
In which keys. Every note of Eb13 belongs to F minor (the ♭VII) and Ab major (the V).
The common shapes, written lowest string first: x65688, x65668, 666688, 11-8-10-8-8-9, 11-10-10-0-9-9, 11-10-10-10-11-9, 11-11-11-12-13-13, 11-13-11-12-13-11.
Under the hand. None of the shapes for Eb13 uses an open string, so every one of them is movable; the lowest sits at the 5th fret. 6 of the 8 need a barre. Together they cover the neck from the 5th fret to the 13th.
Where it goes. Eb13 is the V of Ab, and that is where it goes if it goes anywhere: the third and the flat seventh are a tritone apart, and both resolve by a semitone into Ab.
Shell. Root, third and seventh: the guide tones fix the quality, so the fifth is dropped. That is what leaves a string free, so pick a tension to put on top. Eb13 has x6x688, 11-x-11-12-13-x.
Drop 2. A close-position chord with the second voice from the top lowered an octave. Sits on four adjacent strings. Eb13 has x3102x, x4554x, x-x-10-8-8-9, 9-10-10-8-x-x, x-x-11-12-13-11, 3415xx, xx1523, xx5648.
Drop 3. The third voice from the top lowered an octave. The dropped voice becomes the bass, which is why a string is skipped. Eb13 has 3x152x, x4x543, 8x564x, x6x688, 9-x-10-8-8-x, x-15-x-12-14-11, 11-x-11-12-13-x, x-10-x-8-13-9.
Rootless. The root left to the bass player. Frees a finger for a tension. Eb13 has x3302x, x4556x, xx8688, x-x-10-10-8-9, x-x-11-12-13-13, x-13-11-12-13-x, x3x021, xx3523.
Tensions. A shell of Eb13, root, third and seventh, leaves a string free, and the tones that belong over it are the #11 (A).
What kind of chord this is. Eb13 is a dominant chord — root, major third, fifth, minor seventh. dominant seventh chords on every root, and what they are for.
The common shapes and the derived voicings come from different places, and both are explained in where the chords and the theory come from.
Shows each chord the way this style would voice it, and marks which of its alternatives belong to the idiom.