On the elliptic curves modulo p

We first prove Sun's three conjectures [Z.H. Sun, On the number of incongruent residues of x4+ax2+bx modulo p, J. Number Theory 119 (2006) 210–241; Z.H. Sun, http://sfb.hytc.edu.cn/xsjl/szh/, 2000, June] on the number of rational points of some elliptic curves over finite fields Fp, which are related to the congruence cubic and quartic residue. And we provide some examples and comments concerning these conjectures.