Virtual Knot 4.9
- 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[6,3,7,4], X[7,5,8,6]]
- 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
- 4.15, 4.29, 4.37, 4.48, 4.61, 4.69, 4.78
- Cabled Jones polynomials
- q-25/2 + 2q-23/2 + 3q-21/2 - 4q-19/2 - 4q-17/2 - 2q-15/2 + 3q-13/2 + 2q-11/2 - 2q-9/2 - q-5/2 + q-3/2 - q-1/2
- - q-25 + 4q-24 - q-23 - 6q-45/2 - 10q-22 - 23q-43/2 - 50q-21 - 72q-41/2 - 88q-20 - 108q-39/2 - 112q-19 - 104q-37/2 - 70q-18 - 11q-35/2 + 43q-17 + 135q-33/2 + 191q-16 + 237q-31/2 + 262q-15 + 235q-29/2 + 180q-14 + 71q-27/2 - 13q-13 - 75q-25/2 - 126q-12 - 140q-23/2 - 129q-11 - 92q-21/2 - 55q-10 - 36q-19/2 - 20q-9 - 11q-17/2 - 4q-8 + 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
- 4.61, 4.69
- Self linking number
- -2