Virtual Knot 4.51
- 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[6,1,7,2], X[5,4,6,3], X[4,8,5,7]]
- 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, 4.17, 4.32, 4.58, 4.71, 4.75
- Cabled Jones polynomials
- - q-11/2 + q-9/2 + 2q-7/2 + 4q-5/2 - q-3/2 - 6q-1/2 - 6q1/2 - q3/2 + 4q5/2 + 2q7/2 + q9/2 - q11/2
- - q-23/2 + 3q-21/2 - 3q-19/2 - 2q-9 + 6q-8 + 2q-15/2 - 4q-7 - 2q-13/2 - 30q-6 - 49q-11/2 - 103q-5 - 142q-9/2 - 150q-4 - 183q-7/2 - 119q-3 - 94q-5/2 + 30q-2 + 134q-3/2 + 219q-1 + 335q-1/2 + 310 + 335q1/2 + 219q1 + 134q3/2 + 30q2 - 94q5/2 - 119q3 - 183q7/2 - 150q4 - 142q9/2 - 103q5 - 49q11/2 - 30q6 - 2q13/2 - 4q7 + 2q15/2 + 6q8 - 2q9 - 3q19/2 + 3q21/2 - q23/2
- Other virtual knots (up to mirrors) with the same cabled Jones polynomials
- none
- Generalized Alexander polynomial
- (- s-1 + 1) t-2 + (s-1 + 1 - 2s) t-1 + (- 2 + s + s2) + (s - s2) t
- Other virtual knots (up to mirrors/inversion) with the same Generalized Alexander polynomial
- 4.6, 4.13, 4.31, 4.46
- Self linking number
- 0