  We describe in terms of generators and relations the ring structure of the
$RO(C_2)$-graded $C_2$-equivariant stable stems $\pi_\star^{C_2}$ modulo the
ideal of all nilpotent elements. As a consequence, we also record the ring
structure of the homotopy groups of the rational $C_2$-equivariant sphere
$\pi_\star^{C_2}(S_\mathbb{Q})$.
