Virtual Knot 4.20
- 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+U4-U3+O4-
- PD presentation
- PD[X[2,8,3,1], X[4,2,5,1], X[6,4,7,3], X[5,7,6,8]]
- Jones polynomial
- - q-3/2 + q-1/2 + 2 - q1
- Other virtual knots (up to mirrors) with the same Jones polynomial
- 4.14, 4.22, 4.34, 4.40, 4.52, 4.60, 4.64
- Cabled Jones polynomials
- - q-11/2 + 2q-9/2 + 3q-7/2 - 5q-3/2 - 5q-1/2 + q1/2 + 3q3/2 + q5/2 - q7/2
- - q-23/2 + 2q-21/2 - 2q-19/2 + 2q-17/2 + 7q-8 + 3q-15/2 - 4q-7 - 7q-13/2 - 23q-6 - 22q-11/2 - 39q-5 - 44q-9/2 - 27q-4 - 23q-7/2 + 17q-3 + 21q-5/2 + 52q-2 + 70q-3/2 + 70q-1 + 76q-1/2 + 36 + 15q1/2 - 16q1 - 31q3/2 - 35q2 - 41q5/2 - 26q3 - 15q7/2 - 5q4 - 3q9/2 - 3q5 + q6 - q7
- Other virtual knots (up to mirrors) with the same cabled Jones polynomials
- none
- Generalized Alexander polynomial
- (s-2 - s-1) t-1 + (- s-2 + 1) + (s-1 - 1) t
- Other virtual knots (up to mirrors/inversion) with the same Generalized Alexander polynomial
- 2.1, 3.2, 3.4, 4.18, 4.27, 4.33, 4.34, 4.38, 4.40, 4.44, 4.49, 4.52, 4.60, 4.88, 4.94
- Self linking number
- -2