2001 Diophantine Sextuples of Low Height

In the 3rd century AD, Diophantus of Alexandria asked the question of finding pairs of rational numbers, such that their product was 1 less than a square, i.e. ab+1 = s^2. He found four such numbers: 1/16, 33/16, 17/4 and 105/16. Subsequent searches by authors such as Phil Gibbs and Andrej Dujella and others have found Diophantine sextuples, or six such rational numbers. One example is [5/4, 5/36, 32/9, 189/4, 665/1521, 3213/676]. Lists of these sextuples have been published or listed online. This table is a collation of known sextuples and newly discovered ones. The table lists 2001 Diophantine sextuples of low height followed by a classification scheme and author attribution.