  We present Painlev{\'e} VI sigma form equations for the general Ising low and
high temperature two-point correlation functions $ C(M,N)$ with $M \leq N $ in
the special case $\nu = -k$ where $\nu = \, \sinh 2E_h/k_BT/\sinh 2E_v/k_BT$.
More specifically four different non-linear ODEs depending explicitly on the
two integers $M $ and $N$ emerge: these four non-linear ODEs correspond to
distinguish respectively low and high temperature, together with $ M+N$ even or
odd. These four different non-linear ODEs are also valid for $M \ge N$ when $
\nu = -1/k$. For the low-temperature row correlation functions $ C(0,N)$ with $
N$ odd, we exhibit again for this selected $\nu = \, -k$ condition, a
remarkable phenomenon of a Painlev\'e VI sigma function being the sum of four
Painlev\'e VI sigma functions having the same Okamoto parameters. We show in
this $\nu = \, -k$ case for $ T < T_c $ and also $ T > T_c$, that $ C(M,N)$
with $ M \leq N $ is given as an $ N \times N$ Toeplitz determinant.
