Abstract
We characterize torsion subgroup of the Jacobian of the curve CA : y 2 = x5 + Ax, where A 6= 0 is 8th power free integer. As an application of our result we show that for any quadruple a1, a2, a3, a4 of pairwise distinct non-zero integers there exists an infinite set of integers D with the property that the Jacobian of CaiD is of positive rank for i = 1, 2, 3, 4.
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