Virtual Knot 4.58
- 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-U3+U2-U4+O3+O4+
- PD presentation
- PD[X[2,8,3,1], X[4,1,5,2], X[3,7,4,6], X[5,8,6,7]]
- Jones polynomial
- - q-3/2 - q-1 + q-1/2 + 3 + q1/2 - q1 - q3/2
- Other virtual knots (up to mirrors) with the same Jones polynomial
- 4.2, 4.6, 4.8, 4.12, 4.17, 4.32, 4.51, 4.71, 4.75
- Cabled Jones polynomials
- - q-11/2 + q-9/2 + 3q-7/2 + 6q-5/2 - q-3/2 - 9q-1/2 - 9q1/2 - q3/2 + 6q5/2 + 3q7/2 + q9/2 - q11/2
- - q-23/2 + 3q-21/2 - 3q-19/2 - 2q-9 + 6q-8 + q-15/2 - 5q-7 - 26q-6 - 40q-11/2 - 91q-5 - 129q-9/2 - 132q-4 - 169q-7/2 - 100q-3 - 89q-5/2 + 27q-2 + 122q-3/2 + 193q-1 + 305q-1/2 + 264 + 305q1/2 + 193q1 + 122q3/2 + 27q2 - 89q5/2 - 100q3 - 169q7/2 - 132q4 - 129q9/2 - 91q5 - 40q11/2 - 26q6 - 5q7 + q15/2 + 6q8 - 2q9 - 3q19/2 + 3q21/2 - q23/2
- Other virtual knots (up to mirrors) with the same cabled Jones polynomials
- none
- Generalized Alexander polynomial
- 0
- Other virtual knots (up to mirrors/inversion) with the same Generalized Alexander polynomial
- 0.1, 3.6, 4.8, 4.16, 4.41, 4.55, 4.56, 4.59, 4.68, 4.71, 4.72, 4.75, 4.76, 4.77, 4.90, 4.98, 4.99, 4.105, 4.108
- Self linking number
- 0