Elliptic Curve Integer Point 6y ~ 2 = X-~ 3-x +6

In this paper,we study the elliptic curve 6y2=X3-X+6, by using algebraic number theory and p-adic analysis method,we find all the solutions (x,y)=(1,±1),(0,±1),(6,±6),(9,±11),(23,±45),(25,±51),(64,±209),(13776,±660099). Meanwhile,we give all the positive solutions (x,y)=(10,6),(24,23),(26,26),(65,105),(13777,330050). satisfying(3x)=8(2y).