Links with 2 components and at most 8 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



-- L2(1)-a
s1s1
Alexander polynomial = t-1

-- L2(1)-b
-s1-s1
Alexander polynomial = -t+1

-- L4(1)-a
s1s2s2s1-s2
Alexander polynomial = -2t+2

-- L4(1)-b
-s1-s1-s1-s1
Alexander polynomial = -t^3+t^2-t+1

-- L5(1)-a
-s1s2-s1-s1s2
Alexander polynomial = -t^3+3t^2-3t+1

-- L5(1)-b
s1-s2s1-s2-s2
Alexander polynomial = -t^3+3t^2-3t+1

-- L6(1)-a
-s1s2-s3s2s1-s2s3s2s2s3
Alexander polynomial = 3t-3

-- L6(1)-b
-s1-s1-s1-s1-s1-s1
Alexander polynomial = -t^5+t^4-t^3+t^2-t+1

-- L6(2)-a
s1s1s1s1s2-s1s2
Alexander polynomial = -2t^3+3t^2-3t+2

-- L6(2)-b
-s1-s2-s2-s2-s2-s1s2
Alexander polynomial = 2t^3-3t^2+3t-2

-- L6(3)-a
-s1s2-s3s2s1s2-s3s2
Alexander polynomial = -t^3+5t^2-5t+1

-- L6(3)-b
s1-s2-s1-s1-s1-s2-s2
Alexander polynomial = 2t^3-4t^2+4t-2

-- L7(1)-a
s1s2-s3s2-s1s3-s2-s2s3-s2
Alexander polynomial = 2t^3-5t^2+5t-2

-- L7(1)-b
s1-s2s1-s2-s2-s2-s2
Alexander polynomial = -t^5+3t^4-3t^3+3t^2-3t+1

-- L7(2)-a
-s1s2-s1-s1s2s2s2
Alexander polynomial = -t^5+3t^4-5t^3+5t^2-3t+1

-- L7(2)-b
-s1s2-s3s2s1-s2s3-s2-s3-s3
Alexander polynomial = 2t^3-7t^2+7t-2

-- L7(3)-a
-s1s2-s3-s3s2s1-s2s3-s2-s3
Alexander polynomial = 2t^3-6t^2+6t-2

-- L7(3)-b
-s1s2-s3-s3s2s1-s2s3-s2-s3
Alexander polynomial = 2t^3-6t^2+6t-2

-- L7(4)-a
s1s1s1-s2s1s1-s2
Alexander polynomial = t^5-3t^4+4t^3-4t^2+3t-1

-- L7(4)-b
-s1s2s2s2-s1s2s2
Alexander polynomial = t^5-3t^4+4t^3-4t^2+3t-1

-- L7(5)-a
s1s1-s2s1s1-s2-s2
Alexander polynomial = -t^5+3t^4-6t^3+6t^2-3t+1

-- L7(5)-b
s1-s2-s3-s3-s3-s2-s1-s2s3-s2
Alexander polynomial = -3t^3+7t^2-7t+3

-- L7(6)-a
-s1-s1s2-s1s2-s1s2
Alexander polynomial = t^5-4t^4+7t^3-7t^2+4t-1

-- L7(6)-b
-s1s2-s1s2-s1-s1s2
Alexander polynomial = t^5-4t^4+7t^3-7t^2+4t-1

-- L7(7)-a
s1s1s1-s2-s1-s1-s2
Alexander polynomial = t^3-t^2+t-1

-- L7(7)-b
s1s2s2s1s2s2s2
Alexander polynomial = -t^5+t^4-t+1

-- L7(8)-a
s1s1-s2-s1-s1-s2-s2
Alexander polynomial = -t^3+3t^2-3t+1

-- L7(8)-b
s1-s2-s3-s3-s3-s2-s1s2s3s2
Alexander polynomial = t^3-3t^2+3t-1

-- L8(1)-a
-s1-s2s3s2s2s1s3s2-s3s4s3-s2s3s2-s4
Alexander polynomial = -4t+4

-- L8(1)-b
-s1-s1-s1-s1-s1-s1-s1-s1
Alexander polynomial = -t^7+t^6-t^5+t^4-t^3+t^2-t+1

-- L8(2)-a
s1s1s1s1s1s1s2-s1s2
Alexander polynomial = -2t^5+3t^4-3t^3+3t^2-3t+2

-- L8(2)-b
s1s2-s3-s2-s2-s2-s2-s1-s3-s2s3-s2
Alexander polynomial = -3t^3+5t^2-5t+3

-- L8(3)-a
-s1s2-s3s2s1s2-s3s4s3-s2s3s2-s4
Alexander polynomial = 2t^3-9t^2+9t-2

-- L8(3)-b
s1-s2-s1-s1-s1-s1-s1-s2-s2
Alexander polynomial = 2t^5-4t^4+5t^3-5t^2+4t-2

-- L8(4)-a
s1s2-s3s2-s1s3s2s2s3-s2s3s3
Alexander polynomial = 4t^3-8t^2+8t-4

-- L8(4)-b
s1-s2-s1-s1-s1-s1-s2-s2-s2
Alexander polynomial = 2t^5-4t^4+6t^3-6t^2+4t-2

-- L8(5)-a
-s1s2s2s2-s3s2s1s2-s3s2
Alexander polynomial = -t^5+5t^4-7t^3+7t^2-5t+1

-- L8(5)-b
-s1-s3s2-s3-s2-s2-s2s1-s2s3-s2-s3
Alexander polynomial = -4t^3+9t^2-9t+4

-- L8(6)-a
-s1-s2s3-s4s3s2s1s3s2-s3s4-s3-s2-s4s3
Alexander polynomial = 2t^3-8t^2+8t-2

-- L8(6)-b
-s1-s2-s2-s2-s3-s3s2s1-s2s3-s2-s3
Alexander polynomial = -3t^3+7t^2-7t+3

-- L8(7)-a
-s1s2-s3s2s1-s3-s3s2-s3s2
Alexander polynomial = -t^5+5t^4-9t^3+9t^2-5t+1

-- L8(7)-b
s1-s2s3-s2-s2-s1-s2-s2s3-s2
Alexander polynomial = t^5-5t^4+9t^3-9t^2+5t-1

-- L8(8)-a
-s1s2s2-s3s2s1-s3s2-s3s2
Alexander polynomial = t^5-5t^4+11t^3-11t^2+5t-1

-- L8(8)-b
s1-s2s3-s2-s2-s1-s2s3-s2s3
Alexander polynomial = -t^5+5t^4-11t^3+11t^2-5t+1

-- L8(9)-a
-s1s2-s3s2s1s2s2-s3s2s2
Alexander polynomial = -t^5+5t^4-8t^3+8t^2-5t+1

-- L8(9)-b
-s1s2-s3s4-s3s2s1-s2-s2-s3-s4-s3s2
Alexander polynomial = -3t^3+11t^2-11t+3

-- L8(10)-a
-s1s2s2-s1-s3s2-s3s2
Alexander polynomial = t^5-5t^4+10t^3-10t^2+5t-1

-- L8(10)-b
s1-s2s3s3-s2-s1-s2s3-s2s3
Alexander polynomial = t^5-5t^4+10t^3-10t^2+5t-1

-- L8(11)-a
-s1-s2s3s3s3-s2s1-s2s3-s2
Alexander polynomial = t^5-5t^4+8t^3-8t^2+5t-1

-- L8(11)-b
s1s1s1s1s2s2-s1s2s2
Alexander polynomial = -2t^5+5t^4-7t^3+7t^2-5t+2

-- L8(12)-a
-s1s2-s1-s3-s3s2s2-s3
Alexander polynomial = -t^5+5t^4-10t^3+10t^2-5t+1

-- L8(12)-b
s1-s2s3-s2-s2-s1-s2s3s3-s2
Alexander polynomial = -t^5+5t^4-10t^3+10t^2-5t+1

-- L8(13)-a
-s1-s2s3-s2s3-s2s1-s2s3-s2
Alexander polynomial = -t^5+6t^4-13t^3+13t^2-6t+1

-- L8(13)-b
-s1s2-s1-s3s2-s3s2-s3
Alexander polynomial = -t^5+6t^4-13t^3+13t^2-6t+1

-- L8(14)-a
-s1s2s3-s2s3s2s1s1s2s2s3-s2
Alexander polynomial = 5t^3-13t^2+13t-5

-- L8(14)-b
s1-s2s3-s2s1-s2s3-s2
Alexander polynomial = -t^5+5t^4-12t^3+12t^2-5t+1

-- L8(15)-a
-s1s2-s3s2s1s2s2-s3-s2-s2
Alexander polynomial = -t^3+3t^2-3t+1

-- L8(15)-b
-s1s2-s3s4s3s2s1-s2-s2s3-s4-s3s2
Alexander polynomial = t^3-3t^2+3t-1

-- L8(16)-a
-s1-s2-s2-s1-s3s2-s3s2
Alexander polynomial = t^3-5t^2+5t-1

-- L8(16)-b
s1s2s3s3s2-s1-s2s3-s2s3
Alexander polynomial = -t^5+3t^4-2t^3+2t^2-3t+1


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