The de Broglie frequency and wavelength of the "superluminar" plane phase wave accompaning a "subluminar" particle moving with speed $\:\upsilon\:$ are(1)
\begin{equation} \nu \boldsymbol{=} \dfrac{E }{h} \boldsymbol{=} \dfrac{\sqrt{\left(m_{\mathrm{o}}c^{2}\right)^{2} \boldsymbol{+}\left(pc\right)^{2}}}{h} \boldsymbol{=}\dfrac{\gamma m_{\mathrm{o}}c^{2}}{h} \tag{01}\label{01}
\end{equation}
\begin{equation} \lambda \boldsymbol{=} \dfrac{h }{p} \boldsymbol{=}\dfrac{h}{\gamma m_{\mathrm{o}}v} \tag{02}\label{02}
\end{equation} where $\:\gamma=\left(1\boldsymbol{-}\dfrac{\upsilon^2}{c^2}\right)^{\boldsymbol{-}1/2}\:$ and $\:m_0\:$ the rest mass.
The plane phase wave "superluminar" speed is \begin{equation} \mathrm w=\lambda\,\nu \boldsymbol{=} \dfrac{c^{2}}{\upsilon} \tag{03}\label{03}
\end{equation}
In the rest frame of the particle
\begin{equation} \nu_{0} \boldsymbol{=} \dfrac{E_{0}}{h} \boldsymbol{=} \dfrac{m_{\mathrm{o}}c^{2}}{h} \tag{04}\label{04}
\end{equation} \begin{equation} \lambda_{0} \boldsymbol{=} \infty \tag{05}\label{05}
\end{equation} \begin{equation} \mathrm w_{0} \boldsymbol{=} \infty \tag{06}\label{06}
\end{equation} that is a uniform in space periodic in time vibration with frequency $\:\nu_{0}$.
EDIT :
responds to the OP's comment
I still don't know a lot of stuff in physics, the only thing I knew in your answer was the square root of the Lorentz gamma. Do you think you maybe dumb it down a little? – Kosh Rai
De Broglie hypothesis :
$^{\prime\prime}$The fundamental idea of [my 1924 thesis] was the following : The fact that, following <PERSON>'s introduction of photons in light waves, one knew that light contains particles which are concentrations of energy incorporated into the wave, suggests that all particles, like the electron, must be transported by a wave into which it is incorporated... My essential idea was to extend to all particles the coexistence of waves and particles discovered by <PERSON> in 1905 in the case of light and photons.$^{\prime\prime}$ $^{\prime\prime}$With every particle of matter with mass $m$ and velocity $\upsilon$ a real wave must be 'associated'$^{\prime\prime}$, related to the momentum by the equation: \begin{equation} \lambda \boldsymbol{=} \dfrac{h}{p}\boldsymbol{=}\dfrac{h}{\gamma m \upsilon} \nonumber
\end{equation} where $\lambda$ is the wavelength, $h$ is the <PERSON> constant, $p$ is the momentum, $m$ is the rest mass, $\upsilon$ is the velocity and $c$ is the speed of light in a vacuum.
Louis de Broglie hypothesis is based on the Special Relativity theory and the associated Lorentz transformations. Note that this picture of a particle with velocity $\upsilon$ and its associated plane phase wave with velocity $\mathrm w=c^2/\upsilon$ is Lorentz invariant, that is the same in any inertial system.
(1) See my answer here : About de Broglie relations, what exactly is E? Its energy of what?. 616