  A collection $ \Delta $ of simple closed curves on an orientable surface is
an algebraic $ k $-system if the algebraic intersection number $\langle
\alpha,\beta \rangle$ is equal to $k $ in absolute value for every $ \alpha ,
\beta \in \Delta $ distinct. Generalizing a theorem of [MRT14] we compute that
the maximum size of an algebraic $k$-system of curves on a surface of genus $g$
is $2g+1$ when $g\ge 3$ or $k$ is odd, and $2g$ otherwise. To illustrate the
tightness in our assumptions, we present a construction of curves pairwise
geometrically intersecting twice whose size grows as $g^2$.
