Virtual Knot 4.65
- 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-U3-O4-U2+O3-U4-
- PD presentation
- PD[X[2,8,3,1], X[5,2,6,1], X[3,6,4,7], 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
- 4.23, 4.41, 4.79
- Cabled Jones polynomials
- - q-21/2 + 2q-19/2 + q-17/2 - 3q-15/2 - 2q-13/2 + q-11/2 + 5q-9/2 - 3q-5/2 - q-3/2 - q-1/2
- q-41/2 - 2q-39/2 + q-37/2 - q-35/2 - 3q-17 - q-33/2 + 3q-16 + 4q-31/2 + 8q-15 + 3q-29/2 + 2q-14 + 2q-27/2 - 16q-13 - 18q-25/2 - 19q-12 - 8q-23/2 + 14q-11 + 18q-21/2 + 30q-10 + 24q-19/2 + 10q-9 - 26q-8 - 28q-15/2 - 21q-7 - 12q-13/2 + 3q-6 + 5q-11/2 + 13q-5 + 14q-9/2 + 7q-4 + 4q-7/2 - 3q-3 - 6q-5/2 - 2q-2 + 4q-1
- Other virtual knots (up to mirrors) with the same cabled Jones polynomials
- none
- Generalized Alexander polynomial
- (- s-2 + s-1) t-3 + (- s-2 + 2s-1 - 1) t-2 + (s-2 - 1) t-1 + (s-2 - 2s-1 + 1) + (- s-1 + 1) t
- Other virtual knots (up to mirrors/inversion) with the same Generalized Alexander polynomial
- 4.21, 4.36
- Self linking number
- 0