On certain remarkable curves of genus five. (Q1890444)

Here the author shows the existence of smooth genus five curves having exactly \(24\) Weierstrass points, which constitute the set of fixed points of \(3\) different elliptic involution, and proves that all such curves are bielliptic double covers of Fermat's quartic. To construct the example he uses the projective geometry of elliptic normal quartics in \(\mathbb P^3\), i.e. the geometry of the smooth complete intersections of two quadric surfaces.