Moduli Space of Tori
Fundamental domain of SL(2,ℤ) in the upper half-plane ℍ
Corresponding torus lattice
Parameter τ = a + bi
Real part a:
0.00
Imaginary part b:
1.20
Rectangular
Square
Hexagonal
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...