Let S be a certain affine algebraic surface over Q such that it admits a regular map to A2/Q. We show that any non-trivial torsion element in the Chow group CH1(S) can be pulled back to ideal classes of quadratic fields whose order can be made as large as possible. This gives an affirmative answer to a question analogous to one raised by Agboola and Pappas, in the case of certain affine algebraic surfaces. Spreading out S over Z and for a closed point P∈A2/Z, we show that the cardinality of a subgroup of the Picard group of the fiber SP remains unchanged when P varies over a Zariski open subset in A2/Z. We also show by constructing an element of odd order n≥3 in the class group of certain imaginary quadratic fields that the Picard group of SP has a subgroup isomorphic to Z/nZ.