How Many Distinct Invariants of the Poincaré Group Can you derive?

[Shubee]

Poincaré lists 8 distinct but elementary invariants in his paper, ON
THE DYNAMICS OF THE ELECTRON. See the equation number 5 and 7 in
http://www.univ-nancy2.fr/poincare/bhp/pdf/hp2007gg.pdf
How many invariants in special relativity are you aware of? How many
distinct invariants of the Poincaré group exist? And how many distinct
invariants of the Poincaré group can you derive?
This is how mathematicians measure the understanding of physicists in
spacetime.

I quote:

"Every geometry is defined by a group of transformations, and the goal
of every geometry is to study invariants of this group." Klein,
Erlanger Program.

"Each type of geometry is the study of the invariants of a group of
transformations; that is, the symmetry transformation of some chosen
space." Stewart and Golubitsky 1993, p. 44.

"A geometry is defined by a group of transformations, and investigates
everything that is invariant under the transformations of this given
group." Weyl 1952, p. 133.

"The geometry of Minkowski space is defined by the Poincaré group."
http://www.everythingimportant.org/relativity/generalized.htm

Shubee
http://www.everythingimportant.org/relativity/special.pdf