Moduli Space of Tori

Fundamental domain of SL(2,ℤ) in the upper half-plane ℍ
Corresponding torus lattice

Parameter τ = a + bi

τ = 0 + 1.2i
|τ| = 1.200
In fund. domain: yes
The fundamental domain:
|τ| ≥ 1, |Re(τ)| ≤ ½
SL(2,ℤ) generators:
T: τ→τ+1, S: τ→-1/τ
Modular invariant j(τ):
computed...