It dates roughly to the same time as his monumental Death and the Maiden Quartet, emerging around three years after his previous attempt to write for the string quartet genre, the Quartettsatz, D 703, that he never finished.
Starting in 1824, Schubert largely turned away from the composition of songs to concentrate on instrumental chamber music.
In addition to the A-minor String Quartet, the Quartet in D minor, the Octet, the Grand Duo and Divertissement a la Hongroise (both for piano duet), and the Sonata for Arpeggione and Piano all date from that year.
In the case of the A-minor Quartet, a motive from the third-movement Minuet becomes the most important melodic figure for the following finale.
[1] Schubert dedicated the work to Schuppanzigh, who served as the first violinist of the string quartet appointed by Beethoven.