Virtual Knot 4.37
- 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 equivalent to its inverse.
- Gauss code
- O1-O2-U1-O3-U4-U2-U3-O4-
- PD presentation
- PD[X[2,8,3,1], X[5,1,6,2], X[6,3,7,4], 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, 4.48, 4.61, 4.69, 4.78
- Cabled Jones polynomials
- - 2q-23/2 + q-21/2 + q-19/2 + 3q-17/2 - q-13/2 - q-11/2 - 2q-9/2 - q-5/2 + q-3/2 - q-1/2
- - q-22 - q-43/2 + q-21 - q-41/2 - 3q-20 - q-39/2 + q-19 + 5q-37/2 + 5q-18 + 5q-35/2 + 6q-17 + q-33/2 - q-16 - 6q-31/2 - 9q-15 - 6q-29/2 - 4q-14 - q-27/2 - q-13 - q-25/2 + 2q-12 + 3q-23/2 + 2q-11 + q-10 + 2q-19/2 + 2q-9 + q-15/2 + q-7 - q-6 + 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-4 - 1) t-2 + (- s-3 + s-2) t-1 + (- s-1 + 1)
- Other virtual knots (up to mirrors/inversion) with the same Generalized Alexander polynomial
- none
- Self linking number
- -2