Concordance crosscap numbers of knots and the Alexander polynomial

For a knot the concordance crosscap number, , is the minimum crosscap number among all knots concordant to . Building on work of G. Zhang, which studied the determinants of knots with , we apply the Alexander polynomial to construct new algebraic obstructions to . With the exception of low crossing number knots previously known to have , the obstruction applies to all but four prime knots of 11 or fewer crossings.