Moduli space of quasimaps from P-1 with two marked points to P(1,1,1,3) and j-invariant

In this paper, we construct toric data of moduli space of quasimaps of degree d from P¹ with two marked points to weighted projective space P(1; 1; 1; 3). With this result, we prove that the moduli space is a　compact toric orbifold. We also determine its Chow ring. Moreover, we give a proof of the conjecture proposed by Jinzenji that a series of intersection numbers of the moduli spaces coincides with expansion coefficients of inverse function of −log(j(T)).