This is the elliptic curve I'm working with in the finite field of mod 37:
$$ y^2 = x^3 - 5x + 8 $$ While trying to generate the set of points in it I noticed that, for $x = 5$,
$$ y^2 = 5^3 - 5\times 5 + 8 \text{ mod 37} = 34 \text{ mod 37} $$
Now there are two numbers that satisfies the above equation, namely, $16$ and $21$. Because, $$ 16^2 = 21^2 = 34 \text{ mod 37} $$
Which value should I choose for the elliptic curve? Would either be good or is there any other rules in this case? TIA.