Trinomials ax8+bx+c with Galois groups of order 1344

Sa？etak Bruin and Elkies ([7]) obtained the curve of genus 2 parametrizing trinomials ax8 + bx + c whose Galois group is contained in G1344 = (？/2)3 ？ G168. They found some rational points of small height and computed the associated trinomials. They conjecture that the only ？-rational points of the hyperelliptic curve Y2 = 2X6 + 28X5 + 196X4 + 784X3 + 1715X2 + 2058X + 2401 are given by (X, Y ) = (0, ± 49), (-1, ± 38), (-3, ± 32), and (-7, ± 196). In this paper we prove that the above points are the only S-integral points with S={2,3,5,7,11,13,17,19}