Virtual Knot 4.53
- 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 equivalent to each other.
- This virtual knot is equivalent to its inverse.
- Gauss code
- O1-O2-U1-O3-U4-U3-O4-U2-
- PD presentation
- PD[X[2,8,3,1], X[7,1,8,2], X[5,3,6,4], X[4,6,5,7]]
- Jones polynomial
- q-5 - 2q-4 - 2q-7/2 + q-3 + 2q-5/2 + q-2
- Other virtual knots (up to mirrors) with the same Jones polynomial
- 4.1, 4.3, 4.7, 4.73
- Cabled Jones polynomials
- - q-29/2 + 2q-27/2 + 2q-25/2 - 3q-23/2 - 4q-21/2 - 2q-19/2 + 7q-17/2 + 4q-15/2 - 3q-11/2 - 3q-9/2 - q-5/2 + q-3/2 - q-1/2
- q-28 - 2q-27 + 2q-26 - q-25 - 6q-49/2 - 4q-24 + 3q-23 + 12q-45/2 + 10q-22 + 16q-43/2 + 15q-21 - 10q-41/2 - 24q-20 - 38q-39/2 - 33q-19 - 16q-37/2 - q-18 + 28q-35/2 + 40q-17 + 44q-33/2 + 35q-16 + 6q-31/2 - 14q-15 - 24q-29/2 - 24q-14 - 22q-27/2 - 18q-13 - 6q-25/2 + 5q-12 + 8q-23/2 + 4q-11 + 2q-21/2 + 4q-10 + 4q-19/2 + 2q-9 + q-8 + 2q-15/2 + q-7 - q-6 + 3q-5 - 4q-4 - 4q-7/2 + 2q-3 + 4q-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-2) t-3 + (- s-3 + s-1) t-2 + (s-2 - 1) t-1 + (- s-1 + 1)
- Other virtual knots (up to mirrors/inversion) with the same Generalized Alexander polynomial
- 4.7, 4.100
- Self linking number
- -4