Virtual Knot 4.52
- 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+U3-U2+O4+
- PD presentation
- PD[X[2,8,3,1], X[6,2,7,1], X[5,3,6,4], 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, 4.40, 4.60, 4.64
- Cabled Jones polynomials
- - q-11/2 + 3q-9/2 + 4q-7/2 - 5q-3/2 - 6q-1/2 - q1/2 + q3/2 + q5/2 + q7/2 + q9/2
- - q-23/2 + 3q-21/2 - 4q-19/2 + 3q-17/2 + 12q-8 + 8q-15/2 - 12q-7 - 20q-13/2 - 66q-6 - 79q-11/2 - 129q-5 - 167q-9/2 - 140q-4 - 138q-7/2 - 25q-3 + 13q-5/2 + 125q-2 + 212q-3/2 + 262q-1 + 318q-1/2 + 241 + 202q1/2 + 95q1 + 25q3/2 - 56q2 - 125q5/2 - 134q3 - 133q7/2 - 105q4 - 82q9/2 - 54q5 - 28q11/2 - 13q6 - 5q13/2 + q7 - 2q15/2 + q8 + 2q9 - q10
- 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, 4.40, 4.44, 4.49, 4.60, 4.88, 4.94
- Self linking number
- -2