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.



Torelli group of a punctured elliptic curve
This group is finitely generated. This is classical, but in any case it follows easily from the much more general results in my paper


Putman, Andrew Cutting and pasting in the Torelli group. Geom. Topol. 11 (2007), 829–865. 


which is devoted to understanding the relationships between various notions of the Torelli group on surfaces with multiple boundary components. The Torelli group you are interested in corresponds (in the notation of my paper) to the partition $\{\{b\_1\},\ldots,\{b\_n\}\}$ of the boundary components $b\_1,\ldots,b\_n$ of the surface.


