Virtual Knot 4.66
- 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[3,6,4,7], X[7,5,8,4]]
- 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, 4.67, 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 + 2q-7/2 + 5q-5/2 - 7q-1/2 - 7q1/2 + q3/2 + 4q5/2 + q7/2
- - q-21/2 + q-19/2 + 3q-17/2 + q-8 + 2q-15/2 + 4q-7 - 5q-13/2 + 11q-6 - q-11/2 + 9q-5 + 14q-9/2 - 41q-4 - 23q-7/2 - 129q-3 - 102q-5/2 - 149q-2 - 130q-3/2 - 13q-1 - 9q-1/2 + 186 + 170q1/2 + 254q1 + 209q3/2 + 133q2 + 104q5/2 - 21q3 - 45q7/2 - 102q4 - 90q9/2 - 80q5 - 68q11/2 - 47q6 - 25q13/2 - 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-2 + (s-2 - 2 + s) t-1 + (- 2s-1 + 1 + s) + (- s-2 + 2 - s) t + (s-1 - s) t2
- Other virtual knots (up to mirrors/inversion) with the same Generalized Alexander polynomial
- 4.24
- Self linking number
- 0