Virtual Knot 4.11
- 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+U2-O4-U3+U4-
- PD presentation
- PD[X[2,8,3,1], X[4,1,5,2], X[6,4,7,3], X[7,5,8,6]]
- Jones polynomial
- - q-5/2 + q-3/2 + q-1
- Other virtual knots (up to mirrors) with the same Jones polynomial
- 2.1, 3.3, 4.4, 4.5, 4.18, 4.28, 4.30, 4.33, 4.38, 4.39, 4.44, 4.45, 4.49, 4.54, 4.62, 4.63, 4.74, 4.83, 4.95, 4.101
- Cabled Jones polynomials
- q-17/2 + q-15/2 + 2q-13/2 - q-11/2 - 3q-9/2 - 3q-7/2 - q-5/2 + 2q-3/2
- - q-35/2 + 3q-33/2 - 4q-15 - 4q-29/2 - 16q-14 - 35q-27/2 - 60q-13 - 81q-25/2 - 110q-12 - 124q-23/2 - 129q-11 - 101q-21/2 - 42q-10 + 36q-19/2 + 137q-9 + 206q-17/2 + 264q-8 + 269q-15/2 + 248q-7 + 162q-13/2 + 73q-6 - 17q-11/2 - 74q-5 - 111q-9/2 - 133q-4 - 112q-7/2 - 95q-3 - 62q-5/2 - 44q-2 - 23q-3/2 - 9q-1 - 5q-1/2 - 2 - q1/2 + q3/2
- Other virtual knots (up to mirrors) with the same cabled Jones polynomials
- none
- Generalized Alexander polynomial
- (s-2 - s-1) t-3 + (- s-3 - 2s-2 + s-1 + 2) t-2 + (s-3 + 2s-2 + s-1 - 3 - s) t-1 + (- s-2 - s-1 + 1 + s)
- Other virtual knots (up to mirrors/inversion) with the same Generalized Alexander polynomial
- none
- Self linking number
- -2