Links with 3 components and at most 9 crossings

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(3)6(1)-a
s1s1-s2s1s1-s2
Alexander polynomial = -t^4+3t^3-4t^2+3t-1

-- L(3)6(1)-b
-s1s2s2-s1s2s2
Alexander polynomial = -t^4+3t^3-4t^2+3t-1

-- L(3)6(1)-c
s1s1-s2s1s1-s2
Alexander polynomial = -t^4+3t^3-4t^2+3t-1

-- L(3)6(1)-d
s1-s2-s3-s3-s2-s1-s2s3-s2
Alexander polynomial = -3t^2+6t-3

-- L(3)6(2)-a
-s1s2-s1s2-s1s2
Alexander polynomial = t^4-4t^3+6t^2-4t+1

-- L(3)6(2)-b
s1-s2s1-s2s1-s2
Alexander polynomial = t^4-4t^3+6t^2-4t+1

-- L(3)6(2)-c
-s1s2-s1s2-s1s2
Alexander polynomial = t^4-4t^3+6t^2-4t+1

-- L(3)6(2)-d
s1-s2s1-s2s1-s2
Alexander polynomial = t^4-4t^3+6t^2-4t+1

-- L(3)6(3)-a
s1s1-s2-s1-s1-s2
Alexander polynomial = -t^2+2t-1

-- L(3)6(3)-b
s1s2s2s1s2s2
Alexander polynomial = t^4-t^3-t+1

-- L(3)6(3)-c
s1s1-s2-s1-s1-s2
Alexander polynomial = -t^2+2t-1

-- L(3)6(3)-d
s1s2-s3-s3s2-s1-s2s3-s2
Alexander polynomial = t^2-2t+1

-- L(3)7(1)-a
-s1-s2s3s3-s2s1-s2s3-s2
Alexander polynomial = -t^4+5t^3-8t^2+5t-1

-- L(3)7(1)-b
s1s1s1s2s2-s1s2s2
Alexander polynomial = 2t^4-5t^3+6t^2-5t+2

-- L(3)7(1)-c
-s1s2-s1-s3s2s2-s3
Alexander polynomial = -t^4+5t^3-8t^2+5t-1

-- L(3)7(1)-d
s1-s2s3-s2-s1-s2s3s3-s2
Alexander polynomial = -t^4+5t^3-8t^2+5t-1

-- L(3)8(1)-a
s1s1s1s1-s2s1s1-s2
Alexander polynomial = -t^6+3t^5-4t^4+4t^3-4t^2+3t-1

-- L(3)8(1)-b
-s1s2s2s2s2-s1s2s2
Alexander polynomial = -t^6+3t^5-4t^4+4t^3-4t^2+3t-1

-- L(3)8(1)-c
-s1s2s2-s3s2s2s1-s2s3-s2-s3
Alexander polynomial = 2t^4-5t^3+6t^2-5t+2

-- L(3)8(1)-d
-s1-s2-s2-s3s2s1-s2-s2-s3-s4-s3s2-s3s4
Alexander polynomial = 5t^2-10t+5

-- L(3)8(2)-a
-s1s2-s3s2s1s3-s2s3s3-s2s3
Alexander polynomial = 2t^4-7t^3+10t^2-7t+2

-- L(3)8(2)-b
s1s2-s3s2-s1s3s3-s2s3s3-s2
Alexander polynomial = 2t^4-7t^3+10t^2-7t+2

-- L(3)8(2)-c
s1s1-s2s1s1-s2-s2-s2
Alexander polynomial = -t^6+3t^5-6t^4+8t^3-6t^2+3t-1

-- L(3)8(2)-d
s1-s2-s3-s3-s3-s3-s2-s1-s2s3-s2
Alexander polynomial = -3t^4+7t^3-8t^2+7t-3

-- L(3)8(3)-a
s1s1s2-s3s2s2s1-s3-s2
Alexander polynomial = 2t^4-7t^3+10t^2-7t+2

-- L(3)8(3)-b
s1s2-s3s2s2-s1s3-s2s3s3-s2
Alexander polynomial = 2t^4-7t^3+10t^2-7t+2

-- L(3)8(3)-c
s1s2-s3s2s2-s1s3-s2s3s3-s2
Alexander polynomial = 2t^4-7t^3+10t^2-7t+2

-- L(3)8(3)-d
s1s2-s3s4-s3-s2-s1-s3-s2-s3s4-s3s2-s3
Alexander polynomial = -t^4+7t^3-12t^2+7t-1

-- L(3)8(4)   (2,2)(2,2)-a
-s1s2-s3s2s1s2s2s3s3s2s2
Alexander polynomial = -3t^4+8t^3-10t^2+8t-3

-- L(3)8(4)   (2,2)(2,22-b
s1-s2s3s4s3-s2-s1-s2s3-s4s3-s2
Alexander polynomial = t^4-8t^3+14t^2-8t+1

-- L(3)8(4)   (2,2)(2,22-c
s1s1-s2-s2s1s1-s2-s2
Alexander polynomial = -t^6+3t^5-7t^4+10t^3-7t^2+3t-1

-- L(3)8(4)   (2,2)(2,22-d
s1-s2-s2-s3-s3-s2-s2-s1-s2s3-s2
Alexander polynomial = -3t^4+8t^3-10t^2+8t-3

-- L(3)8(5)-a
-s1-s1-s1s2-s1s2-s1s2
Alexander polynomial = t^6-4t^5+7t^4-8t^3+7t^2-4t+1

-- L(3)8(5)-b
-s1s2-s3s2s1-s2s3-s2s3-s2s3
Alexander polynomial = -2t^4+8t^3-12t^2+8t-2

-- L(3)8(5)-c
-s1s2-s1s2-s1-s1-s1s2
Alexander polynomial = t^6-4t^5+7t^4-8t^3+7t^2-4t+1

-- L(3)8(5)-d
s1s2-s3s2-s1s3-s2s3-s2s3-s2
Alexander polynomial = -2t^4+8t^3-12t^2+8t-2

-- L(3)8(6)-a
-s1s2s3-s2s3s2-s1-s2s3s2s2
Alexander polynomial = 2t^4-9t^3+14t^2-9t+2

-- L(3)8(6)-b
-s1-s1s2-s1s2s2-s1s2
Alexander polynomial = -t^6+4t^5-8t^4+10t^3-8t^2+4t-1

-- L(3)8(6)-c
s1-s2-s2-s3s2s1-s2-s3s2-s3-s2
Alexander polynomial = 2t^4-9t^3+14t^2-9t+2

-- L(3)8(6)-d
-s1s2s2-s1s2-s1-s1s2
Alexander polynomial = -t^6+4t^5-8t^4+10t^3-8t^2+4t-1

-- L(3)8(7)-a
s1s1s1s1-s2-s1-s1-s2
Alexander polynomial = -t^4+t^3+t-1

-- L(3)8(7)-b
s1s2s2s1s2s2s2s2
Alexander polynomial = t^6-t^5-t+1

-- L(3)8(7)-c
-s1-s2-s2-s3s2s2s1-s2s3-s2-s3
Alexander polynomial = t^2-2t+1

-- L(3)8(7)-d
-s1-s2-s2-s3s2s1-s2-s2-s3-s4s3s2s3s4
Alexander polynomial = -t^2+2t-1

-- L(3)8(8)-a
-s1s2-s3s2s1s3-s2-s3-s3-s2s3
Alexander polynomial = 3t^2-6t+3

-- L(3)8(8)-b
s1s2-s3s2-s1s3s3s2s3s3s2
Alexander polynomial = -2t^4+3t^3-2t^2+3t-2

-- L(3)8(8)-c
s1s1-s2-s1-s1-s2-s2-s2
Alexander polynomial = -t^4+3t^3-4t^2+3t-1

-- L(3)8(8)-d
s1-s2-s3-s3-s3-s3-s2-s1s2s3s2
Alexander polynomial = t^4-3t^3+4t^2-3t+1

-- L(3)8(9)   (2,2)(2,2-)-a
-s1s2-s3s2s1-s2-s2s3s3s2s2
Alexander polynomial = t^4-4t^3+6t^2-4t+1

-- L(3)8(9)   (2,2)(2,22-b
s1-s2s3s4s3-s2-s1s2s3-s4s3s2
Alexander polynomial = -t^4+4t^3-6t^2+4t-1

-- L(3)8(9)   (2,2)(2,22-c
s1s1-s2-s2-s1-s1-s2-s2
Alexander polynomial = -t^4+4t^3-6t^2+4t-1

-- L(3)8(9)   (2,2)(2,22-d
s1-s2-s2-s3-s3-s2-s2-s1s2s3s2
Alexander polynomial = t^4-4t^3+6t^2-4t+1

-- L(3)8(10)  (2,2)-(2,2)-a
-s1s2-s3s2s1-s2-s2s3s3-s2-s2
Alexander polynomial = t^4-2t^2+1

-- L(3)8(10)  (2,2)-(2,2-b
s1s2s3s4s3s2-s1s2s3-s4s3s2
Alexander polynomial = t^4-2t^2+1

-- L(3)8(10)  (2,2)-(2,2-c
-s1-s1-s2-s2-s1-s1-s2-s2
Alexander polynomial = t^6-t^5-t^4+2t^3-t^2-t+1

-- L(3)8(10)  (2,2)-(2,2-d
s1-s2-s2-s3-s2-s2-s1s2s3s3s2
Alexander polynomial = t^4-2t^2+1

-- L(3)9(1)-a
-s1s2s2-s3s2s1s2s2-s3s2s2
Alexander polynomial = t^6-5t^5+10t^4-12t^3+10t^2-5t+1

-- L(3)9(1)-b
-s1s2-s3s4-s3s2s2s1-s2-s2-s3-s4-s3s2
Alexander polynomial = 3t^4-11t^3+16t^2-11t+3

-- L(3)9(1)-c
-s1s2s2-s1-s3s2-s3s2s2
Alexander polynomial = -t^6+5t^5-10t^4+12t^3-10t^2+5t-1

-- L(3)9(1)-d
s1-s2s3s3-s2-s1-s2s3-s2s3s3
Alexander polynomial = -t^6+5t^5-10t^4+12t^3-10t^2+5t-1

-- L(3)9(2)-a
-s1s2-s3s2s1-s3s2s2-s3s2s2
Alexander polynomial = -t^6+5t^5-12t^4+16t^3-12t^2+5t-1

-- L(3)9(2)-b
s1-s2-s3s4-s3-s3-s2-s1-s2s3-s2s4
Alexander polynomial = -3t^4+13t^3-20t^2+13t-3

-- L(3)9(2)-c
-s1s2s2-s1-s3-s3s2-s3s2
Alexander polynomial = t^6-5t^5+12t^4-16t^3+12t^2-5t+1

-- L(3)9(2)-d
s1-s2s3s3-s2-s1-s2-s2s3-s2s3
Alexander polynomial = t^6-5t^5+12t^4-16t^3+12t^2-5t+1

-- L(3)9(3)-a
-s1-s2s3s3s3-s2s1-s2s3s3-s2
Alexander polynomial = -t^6+5t^5-10t^4+12t^3-10t^2+5t-1

-- L(3)9(3)-b
-s1s2s2s2-s1-s3s2s2-s3
Alexander polynomial = -t^6+5t^5-10t^4+12t^3-10t^2+5t-1

-- L(3)9(3)-c
-s1s2s2s3s2s2s1s2s2-s3s2s2s2
Alexander polynomial = -2t^6+6t^5-9t^4+10t^3-9t^2+6t-2

-- L(3)9(3)-d
s1-s2s3s3-s2-s1-s2s3s3s3-s2
Alexander polynomial = -t^6+5t^5-10t^4+12t^3-10t^2+5t-1

-- L(3)9(4)-a
-s1s2s2-s1-s3-s3s2s2-s3
Alexander polynomial = t^6-5t^5+12t^4-16t^3+12t^2-5t+1

-- L(3)9(4)-b
s1-s2s3s3-s2-s1-s2-s2s3s3-s2
Alexander polynomial = t^6-5t^5+12t^4-16t^3+12t^2-5t+1

-- L(3)9(4)-c
s1-s2s3s3-s2-s2-s1-s2s3s3-s2
Alexander polynomial = t^6-5t^5+12t^4-16t^3+12t^2-5t+1

-- L(3)9(4)-d
s1s2-s3-s4-s4-s4-s3-s2-s1-s3-s2-s3s4-s3s2-s3
Alexander polynomial = 4t^4-13t^3+18t^2-13t+4

-- L(3)9(5)-a
-s1-s2s3s3s3s3-s2s1-s2s3-s2
Alexander polynomial = -t^6+5t^5-8t^4+8t^3-8t^2+5t-1

-- L(3)9(5)-b
s1s1s1s1s1s2s2-s1s2s2
Alexander polynomial = 2t^6-5t^5+7t^4-8t^3+7t^2-5t+2

-- L(3)9(5)-c
-s1-s2s3-s2s1-s4s3s3s2-s3s4-s3-s2-s4
Alexander polynomial = 2t^4-9t^3+14t^2-9t+2

-- L(3)9(5)-d
s1-s2s3s3-s2-s1s4-s3s2-s3-s2-s4s3-s2
Alexander polynomial = 2t^4-9t^3+14t^2-9t+2

-- L(3)9(6)-a
-s1-s2s3-s4s3s2s1s4-s3s2-s3s4-s3-s2-s3s4
Alexander polynomial = 2t^4-11t^3+18t^2-11t+2

-- L(3)9(6)-b
s1s2-s3s2-s1s3s3s2s2s2s3s3-s2
Alexander polynomial = -4t^4+11t^3-14t^2+11t-4

-- L(3)9(6)-c
-s1s2-s1-s3-s3-s3s2s2-s3
Alexander polynomial = -t^6+5t^5-10t^4+12t^3-10t^2+5t-1

-- L(3)9(6)-d
s1-s2s3-s2-s2-s2-s1-s2s3s3-s2
Alexander polynomial = -t^6+5t^5-10t^4+12t^3-10t^2+5t-1

-- L(3)9(7)-a
-s1-s2-s3s4s4-s3s2s1-s3-s2s4s3-s4s3s2-s3
Alexander polynomial = 2t^4-9t^3+14t^2-9t+2

-- L(3)9(7)-b
-s1s2s2-s3s2s1-s2s3s3s2s2s2s3
Alexander polynomial = -3t^4+9t^3-12t^2+9t-3

-- L(3)9(7)-c
-s1s2-s3s2s1-s2-s4s3s3-s2-s4s3
Alexander polynomial = 2t^4-9t^3+14t^2-9t+2

-- L(3)9(7)-d
s1s2s3-s4s3-s2-s1s4-s3-s2-s3s4s4-s3s2-s3
Alexander polynomial = 2t^4-9t^3+14t^2-9t+2

-- L(3)9(8)   (2,2+)(2,2)-a
-s1s2-s3-s3s2s1s2s2-s3s2s2
Alexander polynomial = -t^6+5t^5-11t^4+14t^3-11t^2+5t-1

-- L(3)9(8)   (2,2+)(2,2-b
s1-s2-s3-s3s4-s3-s2-s1-s2s3-s2s4
Alexander polynomial = -3t^4+12t^3-18t^2+12t-3

-- L(3)9(8)   (2,2+)(2,4-c
s1s1-s2s1s1s3-s2-s2s3
Alexander polynomial = -t^6+5t^5-11t^4+14t^3-11t^2+5t-1

-- L(3)9(8)   (2,2+)(2,3-d
s1s2s3-s4-s4s3-s2-s1-s4-s3-s2-s3s4-s3s2-s3
Alexander polynomial = -3t^4+12t^3-18t^2+12t-3

-- L(3)9(9)   (2,2)1(2,2)-a
-s1-s2s3s3-s2s1s3-s2s3s3-s2
Alexander polynomial = -t^6+5t^5-11t^4+14t^3-11t^2+5t-1

-- L(3)9(9)   (2,2)1(2,2-b
-s1s2s2-s3s2-s1s2s2-s3
Alexander polynomial = -t^6+5t^5-11t^4+14t^3-11t^2+5t-1

-- L(3)9(9)   (2,2)1(2,3-c
-s1s2s2-s1-s3s2s2-s3s2
Alexander polynomial = -t^6+5t^5-11t^4+14t^3-11t^2+5t-1

-- L(3)9(9)   (2,2)1(2,2-d
s1-s2s3s3-s2-s1-s2s3s3-s2s3
Alexander polynomial = -t^6+5t^5-11t^4+14t^3-11t^2+5t-1

-- L(3)9(10)-a
-s1s2-s3s2-s3s2s1s2-s3s2-s3
Alexander polynomial = t^6-6t^5+15t^4-20t^3+15t^2-6t+1

-- L(3)9(10)-b
-s1-s2s3-s2s3-s2s1-s2s3-s2-s2
Alexander polynomial = -t^6+6t^5-15t^4+20t^3-15t^2+6t-1

-- L(3)9(10)-c
s1-s2s1-s2s3-s2s3-s2s3
Alexander polynomial = t^6-6t^5+15t^4-20t^3+15t^2-6t+1

-- L(3)9(10)-d
-s1s2-s3s2-s1-s3s2-s1-s3
Alexander polynomial = -t^6+6t^5-15t^4+20t^3-15t^2+6t-1

-- L(3)9(11)-a
-s1s2s3-s2s3s2s1s1s1s2s2s3-s2
Alexander polynomial = -5t^4+15t^3-20t^2+15t-5

-- L(3)9(11)-b
-s1-s2s3-s2-s2s3-s2s1-s2s3-s2
Alexander polynomial = -t^6+6t^5-14t^4+18t^3-14t^2+6t-1

-- L(3)9(11)-c
s1s1-s2s3-s2s1-s2s3-s2
Alexander polynomial = t^6-5t^5+14t^4-20t^3+14t^2-5t+1

-- L(3)9(11)-d
-s1s2-s1-s3s2-s3-s3s2-s3
Alexander polynomial = -t^6+6t^5-14t^4+18t^3-14t^2+6t-1

-- L(3)9(12)  .(2,2)-a
-s1-s2s3-s2s3-s2s1-s2s3s3-s2
Alexander polynomial = t^6-6t^5+15t^4-20t^3+15t^2-6t+1

-- L(3)9(12)  .(2,2)-b
-s1s2-s3s2-s1-s3s2s2-s3
Alexander polynomial = t^6-6t^5+15t^4-20t^3+15t^2-6t+1

-- L(3)9(12)  .(2,2)-c
-s1s2s2-s1-s3s2-s3s2-s3
Alexander polynomial = t^6-6t^5+15t^4-20t^3+15t^2-6t+1

-- L(3)9(12)  .(2,2)-d
s1-s2s3s3-s2-s1-s2s3-s2s3-s2
Alexander polynomial = t^6-6t^5+15t^4-20t^3+15t^2-6t+1

-- L(3)9(13)-a
-s1s2s2-s3s2s1s2s2-s3-s2-s2
Alexander polynomial = t^4-3t^3+4t^2-3t+1

-- L(3)9(13)-b
-s1-s2-s2-s1-s3s2-s3s2s2
Alexander polynomial = -t^4+3t^3-4t^2+3t-1

-- L(3)9(13)-c
s1s2s3s3s2-s1-s2s3-s2s3s3
Alexander polynomial = t^6-3t^5+2t^4+2t^2-3t+1

-- L(3)9(14)-a
-s1s2-s3s2s1-s3s2s2-s3-s2-s2
Alexander polynomial = -t^4+5t^3-8t^2+5t-1

-- L(3)9(14)-b
-s1-s2-s2-s1-s3-s3s2-s3s2
Alexander polynomial = t^4-5t^3+8t^2-5t+1

-- L(3)9(14)-c
s1s2s3s3s2-s1-s2-s2s3-s2s3
Alexander polynomial = -t^6+3t^5-4t^4+4t^3-4t^2+3t-1

-- L(3)9(15)-a
-s1-s2s3s3s3-s2s1-s2-s3-s3-s2
Alexander polynomial = -2t^4+5t^3-6t^2+5t-2

-- L(3)9(15)-b
s1s2s2s1-s3s2s2s2-s3
Alexander polynomial = t^6-3t^5+4t^4-4t^3+4t^2-3t+1

-- L(3)9(15)-c
-s1-s2-s2s3s2s2s1s2s2-s3s2s2s2
Alexander polynomial = t^6-3t^5+4t^4-4t^3+4t^2-3t+1

-- L(3)9(15)-d
s1-s2s3s3-s2-s1s2s3s3s3s2
Alexander polynomial = t^6-3t^5+4t^4-4t^3+4t^2-3t+1

-- L(3)9(16)-a
-s1-s2-s2-s1-s3-s3s2s2-s3
Alexander polynomial = 2t^4-7t^3+10t^2-7t+2

-- L(3)9(16)-b
s1s2s3s3s2-s1-s2-s2s3s3-s2
Alexander polynomial = -t^6+3t^5-6t^4+8t^3-6t^2+3t-1

-- L(3)9(16)-c
s1-s2-s3-s3-s2-s2-s1-s2s3s3-s2
Alexander polynomial = 2t^4-7t^3+10t^2-7t+2

-- L(3)9(17)-a
-s1-s2s3s3s3-s2s1s2-s3-s3s2
Alexander polynomial = t^2-2t+1

-- L(3)9(17)-b
s1-s2-s2s1-s3s2s2s2-s3
Alexander polynomial = t^2-2t+1

-- L(3)9(17)-c
-s1-s2-s2s3-s2-s2s1s2s2-s3s2s2s2
Alexander polynomial = t^2-2t+1

-- L(3)9(17)-d
s1s2s3s3s2-s1s2s3s3s3s2
Alexander polynomial = -t^6+t^5+2t^4-4t^3+2t^2+t-1

-- L(3)9(18)  (2,2+)(2,2-)-a
-s1s2-s3-s3s2s1s2s2-s3-s2-s2
Alexander polynomial = -t^4+4t^3-6t^2+4t-1

-- L(3)9(18)  (2,2+)(2,2-b
s1s1-s2-s1-s1s3-s2-s2s3
Alexander polynomial = -t^4+4t^3-6t^2+4t-1

-- L(3)9(19)  (2,2+)-(2,2)-a
-s1s2-s3-s3s2s1-s2-s2-s3-s2-s2
Alexander polynomial = t^6-3t^5+3t^4-2t^3+3t^2-3t+1

-- L(3)9(19)  (2,2+)-(22-b
-s1-s1-s2-s1-s1s3-s2-s2s3
Alexander polynomial = t^6-3t^5+3t^4-2t^3+3t^2-3t+1

-- L(3)9(20)  .(2,2-)-a
-s1-s2s3-s2s3-s2s1-s2-s3-s3-s2
Alexander polynomial = 2t^4-8t^3+12t^2-8t+2

-- L(3)9(20)  .(2,2-)-b
s1s2s2s1-s3s2-s3s2-s3
Alexander polynomial = -t^6+4t^5-7t^4+8t^3-7t^2+4t-1

-- L(3)9(20)  .(2,2-)-c
-s1-s2-s2-s1-s3s2-s3s2-s3
Alexander polynomial = 2t^4-8t^3+12t^2-8t+2

-- L(3)9(20)  .(2,2-)-d
s1s2s3s3s2-s1-s2s3-s2s3-s2
Alexander polynomial = -t^6+4t^5-7t^4+8t^3-7t^2+4t-1

-- L(3)9(21)  .-(2,2)-a
-s1-s2s3-s2s3-s2s1s2-s3-s3s2
Alexander polynomial = 0

-- L(3)9(21)  .-(2,2)-b
s1-s2-s2s1-s3s2-s3s2-s3
Alexander polynomial = 0

-- L(3)9(21)  .-(2,2)-c
s1s2-s3s2s1-s3-s2-s2-s3
Alexander polynomial = 0

-- L(3)9(21)  .-(2,2)-d
s1s2-s3-s3s2-s1-s2s3-s2s3-s2
Alexander polynomial = 0


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