Virtual Knot 4.25
- 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-O4-U2-U4-U3-
- PD presentation
- PD[X[2,8,3,1], X[5,1,6,2], X[7,3,8,4], X[6,4,7,5]]
- Jones polynomial
- - q-9/2 + q-7/2 + q-3 - q-5/2 - q-2 + q-3/2 + q-1
- Other virtual knots (up to mirrors) with the same Jones polynomial
- 4.43, 4.80
- Cabled Jones polynomials
- - q-27/2 + 2q-25/2 + 2q-23/2 - 2q-21/2 - 5q-19/2 + 5q-15/2 + 3q-13/2 - 2q-11/2 - 2q-9/2 - q-5/2 - q-1/2
- - q-53/2 + 2q-51/2 - 2q-49/2 + 2q-47/2 + 6q-23 + 2q-45/2 - 4q-22 - 6q-43/2 - 21q-21 - 19q-41/2 - 25q-20 - 25q-39/2 + 10q-19 + 18q-37/2 + 67q-18 + 66q-35/2 + 59q-17 + 61q-33/2 - 7q-16 - 20q-31/2 - 85q-15 - 95q-29/2 - 67q-14 - 63q-27/2 + 5q-13 + 20q-25/2 + 49q-12 + 57q-23/2 + 29q-11 + 25q-21/2 - 3q-10 - 12q-19/2 - 10q-9 - 10q-17/2 - 3q-8 - 4q-15/2 - q-7 + 3q-13/2 + 2q-6 - q-11/2 + 2q-4 + 2q-7/2 - 2q-5/2 - q-2 + 2q-3/2 + 2q-1
- Other virtual knots (up to mirrors) with the same cabled Jones polynomials
- none
- Generalized Alexander polynomial
- (- s-4 + s-3) t-4 + (s-4 - s-3) t-3 + (s-2 - s-1) t-2 + (- s-2 + s-1) t-1
- Other virtual knots (up to mirrors/inversion) with the same Generalized Alexander polynomial
- none
- Self linking number
- -4