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. Terasoma's work is introduced to approximate the direct image connection π∗(∇) by a sequence of regular connections as an intermediate step where π:U→A1=Speck[y], (x,y)↦y. Finally, we will make the comparison of the period obtained by this approximation and that ∇ over U.