Virtual Knot 4.48
- 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-U4-U3-U2-O4-
- PD presentation
- PD[X[2,8,3,1], X[6,1,7,2], X[5,3,6,4], X[4,7,5,8]]
- 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, 4.61, 4.69, 4.78
- Cabled Jones polynomials
- q-25/2 + q-21/2 - 2q-19/2 + q-13/2 - 2q-9/2 - q-5/2 + q-3/2 - q-1/2
- - q-25 + 2q-24 + q-23 - 2q-45/2 + q-22 - 5q-43/2 - 13q-21 - 25q-41/2 - 42q-20 - 48q-39/2 - 60q-19 - 52q-37/2 - 48q-18 - 21q-35/2 + 12q-17 + 48q-33/2 + 73q-16 + 84q-31/2 + 104q-15 + 104q-29/2 + 91q-14 + 53q-27/2 + 32q-13 + 6q-25/2 - 20q-12 - 45q-23/2 - 55q-11 - 49q-21/2 - 45q-10 - 34q-19/2 - 25q-9 - 12q-17/2 - 6q-8 - 2q-15/2 + 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 - s-2 + s-1) t-3 + (- s-3 + 2s-2 - 1) t-2 + (s-3 - s-1) t-1 + (- s-2 + 1)
- Other virtual knots (up to mirrors/inversion) with the same Generalized Alexander polynomial
- none
- Self linking number
- -2