Computing Weierstrass points on the Klein plane curve Let $K:X^3Y+Y^3Z+Z^3X=0$ be the Klein plane curve over $\mathbb{C}$.
I want to calculate Weierstrass points over the curve.
I know that the curve has $168$ automorphisms and I "happen to" find a Weierstrass point $P=(1:0:0)$ whose gap sequence is $1, 2 ,4$.
Since automorphisms permutate Weierstrass points having the same gap sequence, $Q=(0:1:0)$ and $R=(0:0:1)$ are also Weierstrass points.
That's the all I have found.
Of course the curve has other Weierstrass points from the Weierstrass weight theorem.
How can I find the rest?
Thanks to help.

The three points you find are inflection points of the curve.
The other inflections points are also Weierstrass points. You get all 24 inflection points by intersecting the curve with its Hessian.
