Virtual Knot 4.56
- 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 equivalent to each other.
- This virtual knot is not equivalent to its inverse.
- Gauss code
- O1-O2+U1-O3+U4-U3+O4-U2+
- PD presentation
- PD[X[2,8,3,1], X[7,2,8,1], X[5,4,6,3], X[4,6,5,7]]
- 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, 4.59, 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-1/2 - q1/2
- q-9 - q-8 - 2q-15/2 - 9q-7 - 18q-13/2 - 31q-6 - 48q-11/2 - 56q-5 - 74q-9/2 - 72q-4 - 62q-7/2 - 49q-3 - 2q-5/2 + 25q-2 + 76q-3/2 + 114q-1 + 130q-1/2 + 160 + 130q1/2 + 114q1 + 76q3/2 + 25q2 - 2q5/2 - 49q3 - 62q7/2 - 72q4 - 74q9/2 - 56q5 - 48q11/2 - 31q6 - 18q13/2 - 9q7 - 2q15/2 - 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, 4.58, 4.59, 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