Virtual Knot 3.3
- 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-U3-U2-O3-
- PD presentation
- PD[X[2,6,3,1], X[4,1,5,2], X[3,5,4,6]]
- Jones polynomial
- - q-5/2 + q-3/2 + q-1
- Other virtual knots (up to mirrors) with the same Jones polynomial
- 2.1, 4.4, 4.5, 4.11, 4.18, 4.28, 4.30, 4.33, 4.38, 4.39, 4.44, 4.45, 4.49, 4.54, 4.62, 4.63, 4.74, 4.83, 4.95, 4.101
- Cabled Jones polynomials
- q-17/2 - q-11/2 - q-5/2 - q-1/2
- - q-18 + q-17 + 2q-33/2 + 5q-16 + 5q-31/2 + 15q-15 + 17q-29/2 + 14q-14 + 12q-27/2 - 8q-13 - 14q-25/2 - 33q-12 - 36q-23/2 - 25q-11 - 23q-21/2 + 2q-10 + 6q-19/2 + 18q-9 + 19q-17/2 + 10q-8 + 8q-15/2 + q-7 + 3q-13/2 + 2q-6 - q-11/2 + 2q-9/2 + 2q-4 - 2q-3 - 2q-5/2 + q-2 + 2q-3/2 + 2q-1
- - q-61/2 + q-59/2 + 5q-57/2 + 15q-55/2 + 36q-53/2 + 85q-51/2 + 155q-49/2 + 231q-47/2 + 234q-45/2 + 107q-43/2 - 137q-41/2 - 400q-39/2 - 519q-37/2 - 441q-35/2 - 214q-33/2 + 41q-31/2 + 190q-29/2 + 235q-27/2 + 188q-25/2 + 117q-23/2 + 59q-21/2 + 13q-19/2 + 7q-17/2 - 4q-15/2 - q-13/2 - 4q-11/2 - q-9/2 + q-7/2 - 3q-5/2 - q-3/2 - 2q-1/2
- Other virtual knots (up to mirrors) with the same cabled Jones polynomials
- none
- Generalized Alexander polynomial
- (- s-3 + s-2) t-3 + (s-3 - 1) t-1 + (- s-2 + 1)
- Other virtual knots (up to mirrors/inversion) with the same Generalized Alexander polynomial
- 4.81
- Self linking number
- -2