Virtual Knot 4.12
- This virtual knot is equivalent to its vertical mirror image.
- This virtual knot is not equivalent to its horizontal mirror image.
- This virtual knot is equivalent to its inverse.
- Gauss code
- O1-O2-U1-O3+U2-O4+U3+U4+
- PD presentation
- PD[X[2,8,3,1], X[4,1,5,2], X[6,4,7,3], X[7,6,8,5]]
- 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, 4.17, 4.32, 4.51, 4.58, 4.71, 4.75
- Cabled Jones polynomials
- - q-11/2 + q-7/2 + 5q-5/2 - 6q-1/2 - 6q1/2 + 5q5/2 + q7/2 - q11/2
- - q-23/2 + 2q-21/2 - q-19/2 - 2q-9 - q-17/2 + q-8 - 2q-15/2 + 3q-13/2 + 9q-6 + 13q-11/2 + 6q-5 + 2q-9/2 - 5q-4 - 15q-7/2 - 26q-3 - 34q-5/2 - 23q-2 - 5q-3/2 + 19q-1 + 39q-1/2 + 46 + 39q1/2 + 19q1 - 5q3/2 - 23q2 - 34q5/2 - 26q3 - 15q7/2 - 5q4 + 2q9/2 + 6q5 + 13q11/2 + 9q6 + 3q13/2 - 2q15/2 + q8 - q17/2 - 2q9 - q19/2 + 2q21/2 - q23/2
- Other virtual knots (up to mirrors) with the same cabled Jones polynomials
- none
- Generalized Alexander polynomial
- (- s-1 + 1) t-2 + (s-2 + 1 - 2s) t-1 + (- s-2 - s-1 + s + s2) + (2s-1 - 1 - s2) t + (- 1 + s) t2
- Other virtual knots (up to mirrors/inversion) with the same Generalized Alexander polynomial
- none
- Self linking number
- 0