Virtual Knot 4.91
- 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 equivalent to each other.
- This virtual knot is equivalent to its inverse.
- Gauss code
- O1-O2-O3-O4-U1-U2-U3-U4-
- PD presentation
- PD[X[4,8,5,1], X[5,1,6,2], X[6,2,7,3], X[7,3,8,4]]
- Jones polynomial
- - q-11/2 + q-9/2 - q-7/2 + q-5/2 + q-2
- Other virtual knots (up to mirrors) with the same Jones polynomial
- 4.100
- Cabled Jones polynomials
- - q-31/2 + q-29/2 - q-27/2 + q-25/2 - q-23/2 + q-21/2 + 3q-19/2 + q-17/2 - q-15/2 - 3q-13/2 - q-11/2 - q-5/2 + q-3/2 - q-1/2
- - q-59/2 + q-57/2 - q-55/2 + q-53/2 - q-51/2 + q-49/2 - q-47/2 + q-45/2 - q-43/2 + q-41/2 + 7q-20 + 6q-39/2 + 5q-19 - q-37/2 - 4q-18 - 3q-35/2 - 11q-17 - 8q-33/2 - 8q-16 + 3q-15 + 3q-29/2 + 5q-14 - 2q-27/2 + 3q-13 + q-25/2 + q-12 + 4q-21/2 + q-7 - q-6 - 2q-11/2 + q-5 + 2q-9/2 - 2q-7/2 + 2q-5/2 + 2q-2
- Other virtual knots (up to mirrors) with the same cabled Jones polynomials
- none
- Generalized Alexander polynomial
- (- s-4 + s-1) t-4 + (s-2 - 1) t-3 + (s-3 - s-1) t-2 + (s-4 - s-2) t-1 + (- s-3 + 1)
- Other virtual knots (up to mirrors/inversion) with the same Generalized Alexander polynomial
- none
- Self linking number
- -4