  We study irreducible ${\rm SL}_2$-representations of twist knots. We first
determine all non-acyclic ${\rm SL}_2(\mathbb{C})$-representations, which turn
out to lie on a line denoted as $x=y$ in $\mathbb{R}^2$. Our main tools are
character variety, Reidemeister torsion, and Chebyshev polynomials. We also
verify a certain common tangent property, which yields a result on the
$L$-functions of universal deformations, that is, the orders of the associated
knot modules. Secondly, we prove that a representation is on the line $x=y$ if
and only if it factors through the $(-3)$-Dehn surgery, and is non-acyclic if
and only if the image of a certain element is of order 3. Finally, we study
absolutely irreducible non-acyclic representations $\overline{\rho}$ over a
finite field with characteristic $p>2$ to concretely determine all non-trivial
$L$-functions $L_{\rho}$ of the universal deformations over a CDVR. We show
among other things that $L_{\rho}$ $\dot{=}$ $k_n(x)^2$ holds for a certain
series $k_n(x)$ of polynomials.
