Virtual Knot 4.23
- 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-U2+U3-U4-
- PD presentation
- PD[X[2,8,3,1], X[5,2,6,1], X[6,3,7,4], X[7,4,8,5]]
- Jones polynomial
- q-7/2 - 2q-5/2 - q-2 + q-3/2 + 2q-1
- Other virtual knots (up to mirrors) with the same Jones polynomial
- 4.41, 4.65, 4.79
- Cabled Jones polynomials
- - q-21/2 + 2q-19/2 - 3q-15/2 + q-13/2 + 3q-11/2 + 3q-9/2 - 4q-7/2 - 4q-5/2 + q-3/2
- q-41/2 - 2q-39/2 + 2q-37/2 - 2q-35/2 - 3q-17 + 5q-16 + 4q-31/2 + 2q-15 - 7q-29/2 - 10q-14 - 4q-27/2 + q-13 + 10q-25/2 + 43q-12 + 53q-23/2 + 56q-11 + 21q-21/2 - 58q-10 - 91q-19/2 - 168q-9 - 144q-17/2 - 123q-8 - 58q-15/2 + 72q-7 + 110q-13/2 + 193q-6 + 159q-11/2 + 135q-5 + 86q-9/2 + q-4 - 19q-7/2 - 67q-3 - 64q-5/2 - 57q-2 - 42q-3/2 - 14q-1 - 13q-1/2 - 4 - 2q1/2 + 2q3/2
- Other virtual knots (up to mirrors) with the same cabled Jones polynomials
- none
- Generalized Alexander polynomial
- (- s-2 + s-1) t-3 + (s-1 - 1) t-2 + (s-2 - s-1) t-1 + (- s-1 + 1)
- Other virtual knots (up to mirrors/inversion) with the same Generalized Alexander polynomial
- 3.1, 4.10, 4.17, 4.19, 4.32, 4.35, 4.42, 4.50, 4.57, 4.67, 4.70, 4.79
- Self linking number
- 0