Virtual Knot 4.21
- 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[5,8,6,7]]
- Jones polynomial
- - q1/2 + q1 + 2q3/2 + q2 - q5/2 - q3
- Other virtual knots (up to mirrors) with the same Jones polynomial
- 4.10, 4.16, 4.24, 4.31, 4.36, 4.50, 4.57, 4.68, 4.70
- Cabled Jones polynomials
- - q1/2 + 3q3/2 - 3q7/2 - 5q9/2 - 2q11/2 + 4q13/2 + 2q15/2 + q17/2 - q19/2
- - 3q1/2 + 3q1 + 2q3/2 - 2q2 - 15q5/2 - 25q3 - 36q7/2 - 62q4 - 66q9/2 - 87q5 - 68q11/2 - 44q6 + 2q13/2 + 78q7 + 104q15/2 + 182q8 + 171q17/2 + 164q9 + 112q19/2 + 28q10 - 2q21/2 - 83q11 - 86q23/2 - 104q12 - 84q25/2 - 42q13 - 30q27/2 - 3q14 - 5q29/2 + 2q15 + 6q31/2 - 2q33/2 - 3q17 + 3q18 - q19
- Other virtual knots (up to mirrors) with the same cabled Jones polynomials
- none
- Generalized Alexander polynomial
- (1 - s) t-1 + (1 - 2s + s2) + (- 1 + s2) t + (- 1 + 2s - s2) t2 + (s - s2) t3
- Other virtual knots (up to mirrors/inversion) with the same Generalized Alexander polynomial
- 4.36, 4.65
- Self linking number
- 0