Virtual Knot 4.40
- 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+U4+U2-U3+O4+
- PD presentation
- PD[X[2,8,3,1], X[5,1,6,2], X[6,4,7,3], X[4,8,5,7]]
- Jones polynomial
- - q-3/2 + q-1/2 + 2 - q1
- Other virtual knots (up to mirrors) with the same Jones polynomial
- 4.14, 4.20, 4.22, 4.34, 4.52, 4.60, 4.64
- Cabled Jones polynomials
- - q-11/2 + 2q-9/2 + 2q-7/2 - q-5/2 - 4q-3/2 - 3q-1/2 + 2q1/2 + 2q3/2 - q7/2
- - q-23/2 + 2q-21/2 - 2q-19/2 + 2q-17/2 + 6q-8 + 2q-15/2 - 4q-7 - 6q-13/2 - 20q-6 - 18q-11/2 - 25q-5 - 26q-9/2 + 7q-4 + 14q-7/2 + 61q-3 + 58q-5/2 + 61q-2 + 64q-3/2 + 9q-1 - 2q-1/2 - 70 - 80q1/2 - 77q1 - 76q3/2 - 18q2 - q5/2 + 42q3 + 49q7/2 + 39q4 + 38q9/2 + 10q5 + q11/2 - 8q6 - 11q13/2 - 6q7 - 7q15/2 - 3q8 - q17/2 + q19/2
- Other virtual knots (up to mirrors) with the same cabled Jones polynomials
- none
- Generalized Alexander polynomial
- (- s-1 + 1) t-1 + (s-1 - s) + (- 1 + s) t
- Other virtual knots (up to mirrors/inversion) with the same Generalized Alexander polynomial
- 2.1, 3.2, 3.4, 4.18, 4.20, 4.27, 4.33, 4.34, 4.38, 4.44, 4.49, 4.52, 4.60, 4.88, 4.94
- Self linking number
- -2