Virtual Knot 4.17
- 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[4,1,5,2], X[6,4,7,3], X[5,8,6,7]]
- Jones polynomial
- - q-3/2 - q-1 + q-1/2 + 3 + q1/2 - q1 - q3/2
- Other virtual knots (up to mirrors) with the same Jones polynomial
- 4.2, 4.6, 4.8, 4.12, 4.32, 4.51, 4.58, 4.71, 4.75
- Cabled Jones polynomials
- - q-11/2 + q-9/2 + 3q-7/2 + 6q-5/2 - 2q-3/2 - 10q-1/2 - 8q1/2 + q3/2 + 7q5/2 + 2q7/2 - q11/2
- - q-23/2 + 3q-21/2 - 3q-19/2 - 2q-9 + 6q-8 + 2q-15/2 - 6q-7 - 4q-13/2 - 29q-6 - 39q-11/2 - 88q-5 - 118q-9/2 - 135q-4 - 150q-7/2 - 114q-3 - 82q-5/2 + 7q-2 + 107q-3/2 + 209q-1 + 294q-1/2 + 319 + 289q1/2 + 221q1 + 108q3/2 + 7q2 - 103q5/2 - 151q3 - 161q7/2 - 145q4 - 111q9/2 - 82q5 - 30q11/2 - 13q6 - q13/2 - 3q7 + q15/2 + 5q8 - 2q9 - 2q19/2 + 2q21/2 - q23/2
- 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, 4.19, 4.23, 4.32, 4.35, 4.42, 4.50, 4.57, 4.67, 4.70, 4.79
- Self linking number
- 0