Virtual Knot 4.2
- This virtual knot is not equivalent to its vertical mirror image.
- This virtual knot is equivalent to its horizontal mirror image.
- This virtual knot is not equivalent to its inverse.
- Gauss code
- O1-O2-U1-U2-O3+O4+U3+U4+
- PD presentation
- PD[X[2,8,3,1], X[3,1,4,2], X[6,5,7,4], X[7,6,8,5]]
- Jones polynomial
- - q-3/2 - q-1 + q-1/2 + 3 + q1/2 - q1 - q3/2
- Other virtual knots (up to mirrors) with the same Jones polynomial
- 4.6, 4.8, 4.12, 4.17, 4.32, 4.51, 4.58, 4.71, 4.75
- Cabled Jones polynomials
- - q-11/2 + q-7/2 + 5q-5/2 - 6q-1/2 - 6q1/2 + 5q5/2 + q7/2 - q11/2
- - q-23/2 + 2q-21/2 - 2q-19/2 - 2q-9 + 4q-8 - 3q-7 - 7q-6 - 21q-11/2 - 53q-5 - 82q-9/2 - 103q-4 - 135q-7/2 - 128q-3 - 98q-5/2 - 18q-2 + 77q-3/2 + 171q-1 + 260q-1/2 + 282 + 260q1/2 + 171q1 + 77q3/2 - 18q2 - 98q5/2 - 128q3 - 135q7/2 - 103q4 - 82q9/2 - 53q5 - 21q11/2 - 7q6 - 3q7 + 4q8 - 2q9 - 2q19/2 + 2q21/2 - q23/2
- Other virtual knots (up to mirrors) with the same cabled Jones polynomials
- none
- Generalized Alexander polynomial
- (- s-1 + 1) t-2 + (- s-2 + 2s-1 + 1 - 2s) t-1 + (s-2 + s-1 - 4 + s + s2) + (- 2s-1 + 1 + 2s - s2) t + (1 - s) t2
- Other virtual knots (up to mirrors/inversion) with the same Generalized Alexander polynomial
- none
- Self linking number
- 0