Virtual Knot 4.31
- This virtual knot is not equivalent to its vertical mirror image.
- This virtual knot is not equivalent to its horizontal mirror image.
- The two mirror images are not equivalent to each other.
- This virtual knot is not equivalent to its inverse.
- Gauss code
- O1-O2-U1-O3+O4-U3+U2-U4-
- PD presentation
- PD[X[2,8,3,1], X[6,1,7,2], X[5,4,6,3], X[7,4,8,5]]
- Jones polynomial
- - q-3 - q-5/2 + q-2 + 2q-3/2 + q-1 - q-1/2
- Other virtual knots (up to mirrors) with the same Jones polynomial
- 4.10, 4.16, 4.21, 4.24, 4.36, 4.50, 4.57, 4.68, 4.70
- Cabled Jones polynomials
- - q-19/2 + q-15/2 + 5q-13/2 + q-11/2 - 3q-9/2 - 5q-7/2 - 3q-5/2 + 2q-3/2 + q1/2
- - q-19 + 2q-18 - 2q-17 - 2q-33/2 + 4q-31/2 - 3q-29/2 - 13q-27/2 - 32q-13 - 80q-25/2 - 110q-12 - 143q-23/2 - 167q-11 - 153q-21/2 - 117q-10 - 20q-19/2 + 69q-9 + 187q-17/2 + 267q-8 + 306q-15/2 + 306q-7 + 247q-13/2 + 176q-6 + 70q-11/2 - 19q-5 - 86q-9/2 - 131q-4 - 140q-7/2 - 135q-3 - 113q-5/2 - 75q-2 - 50q-3/2 - 21q-1 - 13q-1/2 - 6 - q1/2 + 4q3/2 - q5/2
- Other virtual knots (up to mirrors) with the same cabled Jones polynomials
- none
- Generalized Alexander polynomial
- (- s-2 + s-1) t-3 + (s-2 + s-1 - 2) t-2 + (- 2s-1 + 1 + s) t-1 + (1 - s)
- Other virtual knots (up to mirrors/inversion) with the same Generalized Alexander polynomial
- 4.6, 4.13, 4.46, 4.51
- Self linking number
- 0