My backgrand is complex geometry,but when I confront complex tori,I feel it is easier to consider it as a compact connected complex Lie group although I just know the definition of Lie group.
Let $X=\mathbb{C}^n/\Lambda$,where $\Lambda$ is the discrete subgroup of maximal rank in $\mathbb{C^n}$ whose entries $(x_1,\ldots,x_n)$ are of the form $x_i=a_i+b_i\sqrt{-1}(a_i,b_i\in\mathbb{Z})$.
I want to calculate the group of all biholomorphic group automorphisms $Aut(X)$.
Geometrically,it is the groups of isomorphisms as complex manifolds fixing zero.When $n=1$,it is intuitive that $Aut(X)=\mathbb{Z}/4\mathbb{Z}$.But when the dimension becomes higher，I feel difficult to set out to calculate $Aut(X)$.
I wonder if this problem is easier from the viewpoint of Lie group.Complex geometrical approach is also welcome!Thanks in advance!

My background is complex geometry, but when I confront complex tori, I feel it is easier to consider it as a compact connected complex Lie group although I just know the definition of Lie group.

Let $X=\mathbb{C}^n/\Lambda$,where $\Lambda$ is the discrete subgroup of maximal rank in $\mathbb{C^n}$ whose entries $(x_1,\ldots,x_n)$ are of the form $x_i=a_i+b_i\sqrt{-1}(a_i,b_i\in\mathbb{Z})$. I want to calculate the group of all biholomorphic group automorphisms $Aut(X)$.

Geometrically, it is the groups of isomorphisms as complex manifolds fixing zero. When $n=1$, it is intuitive that $Aut(X)=\mathbb{Z}/4\mathbb{Z}$. But when the dimension becomes higher，I feel difficult to set out to calculate $Aut(X)$.

I wonder if this problem is easier from the viewpoint of Lie group. Complex geometrical approach is also welcome! Thanks in advance!