Can't draw bode curve of this zero
Rewritten in standard form, \$s^2 +\frac{1}{LC}\$ is: -

$$s^2 +\omega_n^2$$ 

Where \$\omega_n\$ is the natural resonant frequency. So equating to zero we find that: -

$$s^2 = -\omega_n^2$$ 

Or

$$s = \pm j\omega_n$$

Because the square root of -1 is either +j or -j

You have a notch filter with zeroes at \$\pm j\omega_n\$