Virtual Knot 4.59
- 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-U3-U2+U4+O3-O4+
- PD presentation
- PD[X[2,8,3,1], X[4,2,5,1], X[3,6,4,7], X[5,8,6,7]]
- Jones polynomial
- 1
- Other virtual knots (up to mirrors) with the same Jones polynomial
- 0.1, 3.1, 3.7, 4.13, 4.19, 4.26, 4.35, 4.42, 4.46, 4.47, 4.55, 4.56, 4.66, 4.67, 4.72, 4.76, 4.77, 4.85, 4.93, 4.96, 4.97, 4.98, 4.102, 4.103, 4.106, 4.107
- Cabled Jones polynomials
- q-7/2 + 2q-5/2 - 4q-1/2 - 4q1/2 + 2q5/2 + q7/2
- q-9 - q-8 - 3q-15/2 - 6q-7 - 8q-13/2 - 22q-6 - 31q-11/2 - 40q-5 - 47q-9/2 - 49q-4 - 50q-7/2 - 27q-3 - 8q-5/2 + 18q-2 + 50q-3/2 + 79q-1 + 97q-1/2 + 98 + 97q1/2 + 79q1 + 50q3/2 + 18q2 - 8q5/2 - 27q3 - 50q7/2 - 49q4 - 47q9/2 - 40q5 - 31q11/2 - 22q6 - 8q13/2 - 6q7 - 3q15/2 - q8 + q9
- Other virtual knots (up to mirrors) with the same cabled Jones polynomials
- none
- Generalized Alexander polynomial
- 0
- Other virtual knots (up to mirrors/inversion) with the same Generalized Alexander polynomial
- 0.1, 3.6, 4.8, 4.16, 4.41, 4.55, 4.56, 4.58, 4.68, 4.71, 4.72, 4.75, 4.76, 4.77, 4.90, 4.98, 4.99, 4.105, 4.108
- Self linking number
- 0