Let $T_{g,n}$ be the Torelli group of a $n$-punctured surface $S=\overline{S}\setminus\{x_1,\ldots,x_n\}$, with $\overline S$ orientable, closed and of genus $g$. By definition, $T_{g,n}$ is the kernel of the following map $$ MCG_{g,n}\hookrightarrow MCG_g\rightarrow {\rm Aut}\big(H_1(\overline S,\mathbb Z), \wedge\big)\simeq Sp_g(\mathbb Z) $$ where $MCG_g$ (reps. $MCG_{g,n}$) stands for the mapping class group of $\overline{S}$ (reps. of $S$) and $\wedge$ denotes the symplectic intersection pairing on $H_1(\overline S,\mathbb Z)$.
Question: What is known about $T_{g,n}$ in the particular case when $g=1$ and $n>0$? Is this group finitely generated? Do we know an explicit system of generators? Etc.
A reference would be welcome.
Thanks for any help.