Virtual Knot 4.7
- 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 equivalent to its inverse.
- Gauss code
- O1-O2-U1-U2-U3-U4-O3-O4-
- PD presentation
- PD[X[2,8,3,1], X[3,1,4,2], X[4,6,5,7], X[5,7,6,8]]
- Jones polynomial
- q-5 - 2q-4 - 2q-7/2 + q-3 + 2q-5/2 + q-2
- Other virtual knots (up to mirrors) with the same Jones polynomial
- 4.1, 4.3, 4.53, 4.73
- Cabled Jones polynomials
- - q-29/2 + 2q-27/2 + 2q-25/2 - 3q-23/2 - 4q-21/2 - 2q-19/2 + 7q-17/2 + 4q-15/2 - 3q-11/2 - 3q-9/2 - q-5/2 + q-3/2 - q-1/2
- q-28 - 2q-27 + 2q-26 - 2q-25 - 6q-49/2 - 3q-24 + 4q-47/2 + 6q-23 + 8q-45/2 + 2q-22 + 2q-43/2 + 13q-21 + 4q-41/2 - 2q-20 - 8q-39/2 - 28q-19 - 52q-37/2 - 115q-18 - 176q-35/2 - 177q-17 - 160q-33/2 - 67q-16 + 28q-31/2 + 147q-15 + 288q-29/2 + 311q-14 + 308q-27/2 + 209q-13 + 116q-25/2 + 29q-12 - 84q-23/2 - 120q-11 - 144q-21/2 - 114q-10 - 90q-19/2 - 71q-9 - 34q-17/2 - 18q-8 - 4q-15/2 - 2q-7 + 2q-6 + 3q-5 - 4q-4 - 4q-7/2 + 2q-3 + 4q-5/2 + 2q-2
- Other virtual knots (up to mirrors) with the same cabled Jones polynomials
- none
- Generalized Alexander polynomial
- (- s-4 + s-3) t-4 + (s-4 - s-2) t-3 + (- s-3 + s-1) t-2 + (s-2 - 1) t-1 + (- s-1 + 1)
- Other virtual knots (up to mirrors/inversion) with the same Generalized Alexander polynomial
- 4.53, 4.100
- Self linking number
- -4