Written out
Every accidental is written in, rather than left to a key signature, so the letters can be read one at a time.
The step pattern
EWF♯HGWAWBWC♯HDWE
What is true of it
E Dorian is E, F♯, G, A, B, C♯ and D, and back to E.
Its steps are W – H – W – W – W – H – W, where W is a whole step and H a half.
On the same tonic, E natural minor differs from it by exactly one note.
Across the first twelve frets of the ukulele its notes fall in 31 places, which is what makes a scale a shape rather than a list.
Chords made only of these notes
C♯dimdiminishedC♯m7♭5half-diminished seventhDmajorDmaj7major seventhEmminorEm7minor seventhF♯mminorF♯m7minor seventh
Found by testing every chord in the catalogue against these 7 sounds, not chosen.