ON THE p-ADIC PERIODS OF THE MODULAR CURVE X(Γ0(p) ∩ Γ(2)).

We prove a variant of Oesterl´e's conjecture describing p-adic periods of the modular curve X₀(p), with an additional Γ(2)-structure (and also Γ(3) ∩ Γ₀(p) if p ≡ 1 (mod 3)). We use de Shalit's techniques and p-adic uniformization of curves with semi-stable reduction. [ABSTRACT FROM AUTHOR]