The integer points on the three elliptic curves y 2 = 4 c x 3 + 13 {y^2} = 4c{x^3} + 13 , c = 1 , 3 , 9 c = 1,3,9 are found, with an application to coding theory. It is also shown that there are precisely three nonisomorphic cubic extensions of the rationals with discriminant − 3 5 ⋅ 13 - {3^5} \cdot 13 .