Let $y^2=x^3+2x+3$ be an elliptic curve over $Bbb{F}_7$. Find all torsion points of order $2$ and $3$ on $E(Bbb{F}_7)$.

Now I used the recursive formula to obtain that the third division polynomial of $E$ is $f_3(x)=3x^4+12x^2+36x-4$.

Calculating the torsion points of order $2$ is fairly easy – they correspond to the points for which $y=0$. So taking $y=0$ one can check and see that the points of order two are $mathcal O, (3,0),(6,0)$.

But how do we find torsion points of order $3$? Does it have any connection with the third division polynomial? (My professor explained that its roots are the $x$ coordinates of the torsion points of order $3$ but I didn’t find this theorem anywhere online).

Every help would be appreciated.