Period determinant of an irregular connection over an elliptic curve

In this article, we calculate the period of an irregular singular connection =d+dy on the Legendre curve U: y2=x(x−1)(x−λ). We calculate its de Rham cohomology and the cycles in the homology of the dual connection and describe the period matrix. Terasomaʹs work is introduced to approximate the direct image connection π*( ) by a sequence of regular connections as an intermediate step where , (x,y) y. Finally, we will make the comparison of the period obtained by this approximation and that over U.