How do you calculate the value of the inductor and capacitor in a parallel LC circuit?
Identify the resonant frequency (f1)
Add a parallel capacitor of known value (Cx).
Measure the resonant frequency again (f2). If it doesn't oscillate try with other capacitor value.
\${f_2 \over f_1} = \sqrt{ C \over {C + C_x}}\$. The only unknown in this is C. You can calculate it.
Determine L using the old frequency and the determined value of C.