Virtual Knot 4.82
- 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-O3-U1-O4-U2-U3-U4-
- PD presentation
- PD[X[3,8,4,1], X[5,1,6,2], X[6,2,7,3], X[7,4,8,5]]
- Jones polynomial
- - q-9/2 - q-4 + q-7/2 + 2q-3 - q-2 + q-1
- Other virtual knots (up to mirrors) with the same Jones polynomial
- 4.87, 4.92, 4.94
- Cabled Jones polynomials
- - q-27/2 + q-23/2 + 5q-21/2 - 4q-19/2 - 5q-17/2 + 2q-15/2 + 5q-13/2 + 2q-11/2 - 6q-9/2 - q-7/2 + q-5/2 - q-1/2
- - q-53/2 + 2q-51/2 - 2q-49/2 - 2q-24 + 4q-23 - 3q-22 - 7q-21 - 11q-41/2 - 25q-20 - 25q-39/2 - q-19 + 4q-37/2 + 39q-18 + 54q-35/2 + 64q-17 + 80q-33/2 + 25q-16 - 4q-31/2 - 65q-15 - 95q-29/2 - 78q-14 - 97q-27/2 - 29q-13 + 9q-25/2 + 49q-12 + 76q-23/2 + 44q-11 + 43q-21/2 + 3q-10 - 12q-19/2 - 14q-9 - 23q-17/2 - 8q-8 - 4q-15/2 + 4q-7 + 6q-13/2 + 3q-6 - 2q-5 - 2q-9/2 + 2q-7/2 + 2q-3 - q-2 + 2q-1
- Other virtual knots (up to mirrors) with the same cabled Jones polynomials
- none
- Generalized Alexander polynomial
- (- s-4 + s-2) t-4 + (s-2 - s-1) t-3 + (s-4 + s-3 - s-2 - s-1) t-2 + (- s-3 - s-2 + 2s-1) t-1
- Other virtual knots (up to mirrors/inversion) with the same Generalized Alexander polynomial
- none
- Self linking number
- -2