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We compute the nonabelian $\mathrm{SL_2}(\mathbb{C})$-character varieties ofthe rational knots $C(2n+1,2m,2)$ in the Conway notation, where $m$ and $n$ arenon-zero integers. By studying real points on these varieties, we determine theleft orderability of the fundamental groups of the cyclic branched covers of$C(2n+1,2m,2)$.

Left orderability of cyclic branched covers of rational knots $C(2n+1,2m,2)$