This table includes the knot designation, followed by the braid representation used by the braid programme, followed by the Alexander polynomial.
Output from braid v5.0.b1
-- L(4)8(1)-a -s1-s2s3s3-s2s1-s2s3s3-s2 Alexander polynomial = t^5-5t^4+10t^3-10t^2+5t-1 -- L(4)8(1)-b -s1s2s2-s1-s3s2s2-s3 Alexander polynomial = t^5-5t^4+10t^3-10t^2+5t-1 -- L(4)8(1)-c -s1s2s2s3s2s2s1s2s2-s3s2s2 Alexander polynomial = 2t^5-6t^4+8t^3-8t^2+6t-2 -- L(4)8(1)-d s1-s2s3s3-s2-s1-s2s3s3-s2 Alexander polynomial = t^5-5t^4+10t^3-10t^2+5t-1 -- L(4)8(1)-e -s1s2s2-s1-s3s2s2-s3 Alexander polynomial = t^5-5t^4+10t^3-10t^2+5t-1 -- L(4)8(1)-f s1-s2s3s3-s2-s1-s2s3s3-s2 Alexander polynomial = t^5-5t^4+10t^3-10t^2+5t-1 -- L(4)8(1)-g s1-s2s3s3-s2-s1-s2s3s3-s2 Alexander polynomial = t^5-5t^4+10t^3-10t^2+5t-1 -- L(4)8(1)-h s1s2-s3-s4-s4-s3-s2-s1-s3-s2-s3s4-s3s2-s3 Alexander polynomial = 4t^3-12t^2+12t-4 -- L(4)8(2)-a -s1-s2s3s3-s2s1-s2-s3-s3-s2 Alexander polynomial = 2t^3-6t^2+6t-2 -- L(4)8(2)-b s1s2s2s1-s3s2s2-s3 Alexander polynomial = -t^5+3t^4-4t^3+4t^2-3t+1 -- L(4)8(2)-c -s1-s2-s2s3s2s2s1s2s2-s3s2s2 Alexander polynomial = -t^5+3t^4-4t^3+4t^2-3t+1 -- L(4)8(2)-d s1-s2s3s3-s2-s1s2s3s3s2 Alexander polynomial = -t^5+3t^4-4t^3+4t^2-3t+1 -- L(4)8(2)-e -s1-s2-s2-s1-s3s2s2-s3 Alexander polynomial = 2t^3-6t^2+6t-2 -- L(4)8(2)-f s1s2s3s3s2-s1-s2s3s3-s2 Alexander polynomial = -t^5+3t^4-4t^3+4t^2-3t+1 -- L(4)8(2)-g s1-s2-s3-s3-s2-s1-s2s3s3-s2 Alexander polynomial = 2t^3-6t^2+6t-2 -- L(4)8(2)-h s1s2s3-s4-s4s3-s2-s1-s3-s2-s3s4-s3s2-s3 Alexander polynomial = -2t^3+6t^2-6t+2 -- L(4)8(3)-a -s1-s2s3s3-s2s1s2-s3-s3s2 Alexander polynomial = 0 -- L(4)8(3)-b s1-s2-s2s1-s3s2s2-s3 Alexander polynomial = 0 -- L(4)8(3)-c -s1-s2-s2s3-s2-s2s1s2s2-s3s2s2 Alexander polynomial = 0 -- L(4)8(3)-d s1s2s3s3s2-s1s2s3s3s2 Alexander polynomial = t^5-t^4-2t^3+2t^2+t-1 -- L(4)8(3)-e s1s2s2s1-s3-s2-s2-s3 Alexander polynomial = 0 -- L(4)8(3)-f s1s2-s3-s3s2-s1-s2s3s3-s2 Alexander polynomial = 0 -- L(4)8(3)-g s1-s2-s3-s3-s2-s1-s2-s3-s3-s2 Alexander polynomial = -t^5+t^4+2t^3-2t^2-t+1 -- L(4)8(3)-h s1s2s3-s4-s4s3-s2-s1s3-s2-s3s4-s3s2s3 Alexander polynomial = 0 -- L(4)9(1)-a -s1-s2-s3s4s4-s3s2s1-s3s2-s3s4-s3-s2-s3 Alexander polynomial = t^5-7t^4+16t^3-16t^2+7t-1 -- L(4)9(1)-b -s1s2s2-s1-s3s2s2s3s3s3 Alexander polynomial = -2t^5+8t^4-14t^3+14t^2-8t+2 -- L(4)9(1)-c -s1s2s2-s3s2s2s1-s2s3s3-s2s3 Alexander polynomial = -2t^5+8t^4-14t^3+14t^2-8t+2 -- L(4)9(1)-d s1s1-s2s1s1-s3s2s2-s3s2 Alexander polynomial = -2t^5+8t^4-14t^3+14t^2-8t+2 -- L(4)9(1)-e -s1-s2s3s3-s2s1-s2-s4s3-s2-s4 Alexander polynomial = t^5-7t^4+16t^3-16t^2+7t-1 -- L(4)9(1)-f s1s2s2-s3s2s2-s1s3-s2s3s3-s2 Alexander polynomial = -2t^5+8t^4-14t^3+14t^2-8t+2 -- L(4)9(1)-g s1-s2s3-s2-s1-s2-s4s3s3-s2-s4 Alexander polynomial = t^5-7t^4+16t^3-16t^2+7t-1 -- L(4)9(1)-h s1s2-s3s4-s3-s2-s1-s3-s2-s3s4s4-s3s2-s3 Alexander polynomial = t^5-7t^4+16t^3-16t^2+7t-1