Virtual Knot 4.67
- 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[7,4,8,5]]
- Jones polynomial
- 1
- Other virtual knots (up to mirrors) with the same Jones polynomial
- 0.1, 3.1, 3.7, 4.13, 4.19, 4.26, 4.35, 4.42, 4.46, 4.47, 4.55, 4.56, 4.59, 4.66, 4.72, 4.76, 4.77, 4.85, 4.93, 4.96, 4.97, 4.98, 4.102, 4.103, 4.106, 4.107
- Cabled Jones polynomials
- - q-9/2 + 3q-5/2 + 2q-3/2 - 3q-1/2 - 5q1/2 - q3/2 + 2q5/2 + q7/2
- - q-21/2 + q-19/2 + 3q-17/2 - 2q-8 - q-15/2 - 2q-7 - 8q-13/2 + 8q-6 - q-11/2 + 33q-5 + 42q-9/2 + 32q-4 + 34q-7/2 - 39q-3 - 46q-5/2 - 122q-2 - 138q-3/2 - 109q-1 - 95q-1/2 + 22 + 63q1/2 + 142q1 + 155q3/2 + 130q2 + 115q5/2 + 47q3 + q7/2 - 38q4 - 53q9/2 - 48q5 - 47q11/2 - 38q6 - 20q13/2 - 12q7 - 4q15/2 - 2q8 + 2q9
- Other virtual knots (up to mirrors) with the same cabled Jones polynomials
- none
- Generalized Alexander polynomial
- (s-1 - 1) t-1 + (- 1 + s) + (- s-1 + 1) t + (1 - s) t2
- Other virtual knots (up to mirrors/inversion) with the same Generalized Alexander polynomial
- 3.1, 4.10, 4.17, 4.19, 4.23, 4.32, 4.35, 4.42, 4.50, 4.57, 4.70, 4.79
- Self linking number
- 0