This is a joint project with Ling Long, Noriko Yui, and Wadim Zudilin. In this project, we study the supercongruences coming from the well-known 14 hypergeometric families of Calabi-Yau 3-folds whose Picard-Fuchs equations are degree 4 hypergeometric differential equations with solution near 0 are the 4F3-hypergeomitric series,

4F3(1/d,1-1/d, 1/t, 1-1/t; 1,1,1; z), d,t =2,3,4,6 or (d,t)=(1/5, 2/5),

(1/8,3/8), (1/10, 3/10), (1/12, 5/12).

When z=1, they are corresponding to rigid Calabi-Yau 3-folds defined over Q. Due to Gouvea and Yui, a rigid Calabi-Yau 3-fold defined over Q is modular. Roriguez-Villegas conjectured the corresponding Hecke eigenforms and identified numerically possible supercongruences. In this talk, I will illustrate the case d=t=3 to give an idea of our proof of the corresponding supercongruences conjectured by Roriguez-Villegas.