Virtual Knot 4.57
- 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-U3-U2-U4+O3-O4+
- PD presentation
- PD[X[2,8,3,1], X[4,1,5,2], X[3,6,4,7], X[5,8,6,7]]
- 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, 4.31, 4.36, 4.50, 4.68, 4.70
- Cabled Jones polynomials
- - q-19/2 + q-17/2 + 3q-15/2 + 5q-13/2 - 3q-11/2 - 7q-9/2 - 4q-7/2 + q-5/2 + 4q-3/2 - q-1/2
- - q-19 + 3q-18 - 3q-17 - 2q-33/2 + 6q-31/2 + q-15 - 6q-29/2 - q-14 - 29q-27/2 - 43q-13 - 93q-25/2 - 130q-12 - 129q-23/2 - 169q-11 - 89q-21/2 - 76q-10 + 53q-19/2 + 149q-9 + 221q-17/2 + 309q-8 + 241q-15/2 + 260q-7 + 131q-13/2 + 73q-6 - 23q-11/2 - 85q-5 - 89q-9/2 - 123q-4 - 87q-7/2 - 98q-3 - 65q-5/2 - 47q-2 - 27q-3/2 - 13q-1 - 13q-1/2 - 2 - q1/2 + q3/2
- Other virtual knots (up to mirrors) with the same cabled Jones polynomials
- none
- Generalized Alexander polynomial
- (- s-2 + s-1) t-2 + (s-1 - 1) t-1 + (s-2 - s-1) + (- s-1 + 1) t
- Other virtual knots (up to mirrors/inversion) with the same Generalized Alexander polynomial
- 3.1, 4.10, 4.17, 4.19, 4.23, 4.32, 4.35, 4.42, 4.50, 4.67, 4.70, 4.79
- Self linking number
- 0