Non-symmetric ribbon conjecture for the family \mathcal{A}$S,T$

Let $\mathcal{A}(S,T)$ be the ribbon-knot family considered in the paper, with parameters $S,T$, and let 12n268 denote the specified knot in the determinant-$9$ table. A symmetric union presentation is a diagram of a knot that is symmetric with respect to an axis. Non-symmetric ribbon conjecture for $\mathcal{A}(S,T)$. With the exception of 12n268 and the knots with $S=-1,0$, the knots $\mathcal{A}(S,T)$ do not have symmetric union presentations. This conjecture is supported by the knots with 13 crossings in the table; the corresponding question remains open for the other members of the family.