Virtual Knot 4.68
- 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+O4+U2+O3+U4+
- PD presentation
- PD[X[2,8,3,1], X[5,2,6,1], X[3,7,4,6], X[7,5,8,4]]
- 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, 4.21, 4.24, 4.31, 4.36, 4.50, 4.57, 4.70
- Cabled Jones polynomials
- q-1/2 - q1/2 - 3q5/2 - 2q7/2 + q11/2 + 3q13/2 - q19/2
- - q-5/2 + 2q-3/2 + q-1/2 - 2 - q1/2 - 3q1 - 9q3/2 - 13q2 - 29q5/2 - 15q3 - 7q7/2 + 24q4 + 42q9/2 + 58q5 + 74q11/2 + 50q6 + 24q13/2 - 30q7 - 57q15/2 - 74q8 - 76q17/2 - 57q9 - 30q19/2 + 7q10 + 29q21/2 + 41q11 + 34q23/2 + 26q12 + 14q25/2 + 9q13 + q27/2 - 8q14 - 7q29/2 - 8q15 - 2q31/2 - 2q16 - 2q33/2 + 2q18 - q19
- 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, 4.58, 4.59, 4.71, 4.72, 4.75, 4.76, 4.77, 4.90, 4.98, 4.99, 4.105, 4.108
- Self linking number
- 0