The knots 6_1 and 9_46 have the same Alexander polynomial. Their Jones polynomials are different, though:
In[1]:= Jones[Knot[6, 3]][q]
Jones[Knot[6, 3]][q]
Out[1]= − q 3 + 2 q 2 − 2 q + 3 − 2 q + 2 q 2 − 1 q 3 {\displaystyle -q^{3}+2q^{2}-2q+3-{\frac {2}{q}}+{\frac {2}{q^{2}}}-{\frac {1}{q^{3}}}}
In[2]:= Jones[Knot[9, 48]][q]
Jones[Knot[9, 48]][q]
Out[2]= − 2 q 6 + 3 q 5 − 4 q 4 + 6 q 3 − 4 q 2 + 4 q − 3 + 1 q {\displaystyle -2q^{6}+3q^{5}-4q^{4}+6q^{3}-4q^{2}+4q-3+{\frac {1}{q}}}
In[3]:= Jones[Knot[10, 112]][q]
Jones[Knot[10, 112]][q]
Out[3]= q 3 − 4 q 2 + 7 q − 10 + 14 q − 14 q 2 + 14 q 3 − 11 q 4 + 7 q 5 − 4 q 6 + 1 q 7 {\displaystyle q^{3}-4q^{2}+7q-10+{\frac {14}{q}}-{\frac {14}{q^{2}}}+{\frac {14}{q^{3}}}-{\frac {11}{q^{4}}}+{\frac {7}{q^{5}}}-{\frac {4}{q^{6}}}+{\frac {1}{q^{7}}}}
