Virtual Knot 4.15
- 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-U2-U4-U3-O4-
- PD presentation
- PD[X[2,8,3,1], X[4,1,5,2], X[6,3,7,4], X[5,7,6,8]]
- 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, 4.29, 4.37, 4.48, 4.61, 4.69, 4.78
- Cabled Jones polynomials
- - q-23/2 + 2q-21/2 + q-17/2 - q-15/2 - 2q-9/2 - q-5/2 + q-3/2 - q-1/2
- - q-22 + q-21 - q-41/2 - q-20 - q-39/2 - 7q-19 - 13q-37/2 - 24q-18 - 28q-35/2 - 31q-17 - 25q-33/2 - 12q-16 - q-31/2 + 24q-15 + 47q-29/2 + 62q-14 + 55q-27/2 + 47q-13 + 36q-25/2 + 18q-12 - 7q-23/2 - 24q-11 - 28q-21/2 - 27q-10 - 23q-19/2 - 19q-9 - 10q-17/2 - 5q-8 - q-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-3 - s-2) t-3 + (s-4 - s-3 - s-2 + s-1) t-2 + (- s-3 + 2s-2 - 1) t-1 + (- s-1 + 1)
- Other virtual knots (up to mirrors/inversion) with the same Generalized Alexander polynomial
- none
- Self linking number
- -2