Consider the families of curves $C^{n,A}:y²=xⁿ+Ax$ and $C_{n,A}:y²=xⁿ+A$ where A is a nonzero rational. Let $J^{n,A}$ and $J_{n,A}$ denote their respective Jacobian varieties. The torsion points of $C^{3,A}\left(\mathbb{Q}\right)$ and $C_{3,A}\left(\mathbb{Q}\right)$ are well known. We show that for any nonzero rational A the torsion subgroup of $J^{7,A}\left(\mathbb{Q}\right)$ is a 2-group, and for A ≠ 4a⁴,-1728,-1259712 this subgroup is equal to $J^{7,A}\left(\mathbb{Q}\right)\left[2\right]$ (for a excluded values of A, with the possible exception of A = -1728, this group has a point of order 4). This is a variant of the corresponding results for $J^{3,A}$ (A ≠ 4) and $J^{5,A}$. We also almost...