Virtual Knot 4.78
- 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-U4-U2-O3-O4-
- PD presentation
- PD[X[2,8,3,1], X[5,1,6,2], X[3,6,4,7], X[4,7,5,8]]
- Jones polynomial
- - q-4 - q-7/2 + q-3 + q-5/2 + q-2
- Other virtual knots (up to mirrors) with the same Jones polynomial
- 4.9, 4.15, 4.29, 4.37, 4.48, 4.61, 4.69
- Cabled Jones polynomials
- - q-23/2 + 4q-21/2 + 2q-19/2 - q-17/2 - 5q-15/2 - 2q-13/2 + 2q-11/2 - q-5/2 + q-3/2 - q-1/2
- - 4q-22 - 3q-43/2 - 9q-21 - 11q-41/2 - 24q-20 - 21q-39/2 - 48q-19 - 49q-37/2 - 75q-18 - 63q-35/2 - 51q-17 - 24q-33/2 + 48q-16 + 67q-31/2 + 153q-15 + 147q-29/2 + 168q-14 + 106q-27/2 + 59q-13 + 22q-25/2 - 42q-12 - 59q-23/2 - 86q-11 - 58q-21/2 - 55q-10 - 38q-19/2 - 27q-9 - 13q-17/2 - 6q-8 - 3q-15/2 + q-5 - 2q-4 - 2q-7/2 + 2q-3 + 2q-5/2 + 2q-2
- Other virtual knots (up to mirrors) with the same cabled Jones polynomials
- none
- Generalized Alexander polynomial
- (- s-4 + s-3) t-4 + (- s-2 + s-1) t-3 + (s-2 - 1) t-2 + (s-4 - s-1) t-1 + (- s-3 + 1)
- Other virtual knots (up to mirrors/inversion) with the same Generalized Alexander polynomial
- none
- Self linking number
- -2