Sufficiency and ancillarity — a regression with one parameter

Let $X_1,X_2,…,X_n$ $(n>5)$ be independent random variables such that $X_t=\alpha+\alpha^2t+\epsilon_t$, for $t=1,…,n$, where $\epsilon_1,\epsilon_2,…,\epsilon_n$ are independent and identically distributed $N(0,\sigma^2)$ random variables. Here $\alpha\in\mathbb{R}$ and $\sigma>0$ are unknown parameters. Which of the following statements are true?