On the volume of double twist link cone-manifolds

We consider the double twist link $J(2m+1, 2n+1)$ which is the two-bridge link corresponding to the continued fraction $(2m+1)-1/(2n+1)$. It is known that $J(2m+1, 2n+1)$ has reducible nonabelian $SL_2(\mathbb C)$-character variety if and only if $m=n$. In this paper we give a formula for the volume of hyperbolic cone-manifolds of $J(2m+1,2m+1)$. We also give a formula for the A-polynomial $2$-tuple corresponding to the canonical component of the character variety of $J(2m+1,2m+1)$.