We got artificially defined curve over $\mathbb{F}_{11}$ of genus $1$ and only two projective points and this contradict the Hasse bound on number of points over finite fields. The curve has only one singular projective point.
For $p=11$ the affine curve is: $$ (1) \qquad x^3-y^3- 1=0 $$ $$ (2) \qquad 1=z x (x-1) (x-2) (x-3) (x-4) (x-5) (x-6) (x-7) (x-8)(x-9) (x-10) $$
(2) is essentially disequality constraint.
What is wrong with this violation of the Hasse bound?
Possible problem could be the singular point, but projective closure of hyperelliptic curve also have singular point.