Integrability of second-order Fuchsian equation on Torus T~2

Consider the differential equationii-λp(t)u=0, (1)where the parameter γ∈R~+, and t∈C u(t)∈C, and ρ(t) is the elliptic function ofWeierstrass with periods ω,=2α and ω=2αi (α∈R). It is shown that ρ(t) has the following properties: (i) ρ(0) =0, (ii) ρ(it)=-ρ(t),t∈C (iii) for any t∈R, ρ(t)∈R and ρ(t)≤0, and for t∈[-α, 0], ρ(t) increases from -1