Virtual Knot 4.69
- 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-O3-U2-U4-
- PD presentation
- PD[X[2,8,3,1], X[6,1,7,2], X[3,5,4,6], X[7,4,8,5]]
- 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, 4.37, 4.48, 4.61, 4.78
- Cabled Jones polynomials
- 3q-21/2 - q-19/2 - q-17/2 - 2q-15/2 + q-13/2 + q-11/2 - 2q-9/2 - q-5/2 + q-3/2 - q-1/2
- q-24 - q-23 - 2q-45/2 - 10q-22 - 17q-43/2 - 29q-21 - 44q-41/2 - 56q-20 - 87q-39/2 - 103q-19 - 120q-37/2 - 116q-18 - 95q-35/2 - 54q-17 + 42q-33/2 + 125q-16 + 203q-31/2 + 253q-15 + 287q-29/2 + 265q-14 + 184q-27/2 + 95q-13 + 17q-25/2 - 47q-12 - 114q-23/2 - 136q-11 - 133q-21/2 - 105q-10 - 84q-19/2 - 64q-9 - 33q-17/2 - 17q-8 - 4q-15/2 - 2q-7 + 2q-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-4 + s-3 - 2s-2) t-3 + (- 2s-3 + 2s-1) t-2 + (2s-2 - s-1 - 1) t-1 + (- s-1 + 1)
- Other virtual knots (up to mirrors/inversion) with the same Generalized Alexander polynomial
- 4.9, 4.61
- Self linking number
- -2