  It is known that there are only finitely many knots with super bridge index
3. Jin and Jeon have provided a list of possible such candidates. However, they
conjectured that the only knots with super bridge index 3 are trefoil and the
figure eight knot. In this paper, we prove that the $5_2$ knot and the $6_2$
knot are also 3-super bridge knots by providing a polynomial representation of
these knots in degree $6.$ This also answers a question asked by Durfee and
O'Shea in their paper on polynomial knots: is there any 5-crossing knot in
degree 6?
