Virtual Knot 4.19
- 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-U2+U4+U3-O4+
- PD presentation
- PD[X[2,8,3,1], X[4,2,5,1], X[6,3,7,4], 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, 4.26, 4.35, 4.42, 4.46, 4.47, 4.55, 4.56, 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-7/2 + 3q-5/2 + q-3/2 - 5q-1/2 - 6q1/2 - q3/2 + 3q5/2 + 2q7/2
- 2q-9 - 2q-8 - 4q-15/2 - 12q-7 - 22q-13/2 - 46q-6 - 69q-11/2 - 90q-5 - 111q-9/2 - 127q-4 - 101q-7/2 - 72q-3 + 15q-5/2 + 66q-2 + 150q-3/2 + 221q-1 + 221q-1/2 + 250 + 170q1/2 + 145q1 + 47q3/2 - 14q2 - 54q5/2 - 106q3 - 107q7/2 - 113q4 - 79q9/2 - 66q5 - 44q11/2 - 27q6 - 9q13/2 - 5q7 - 3q15/2 - q8 + q9
- Other virtual knots (up to mirrors) with the same cabled Jones polynomials
- none
- Generalized Alexander polynomial
- (- s-1 + 1) t-2 + (1 - s) t-1 + (s-1 - 1) + (- 1 + s) t
- Other virtual knots (up to mirrors/inversion) with the same Generalized Alexander polynomial
- 3.1, 4.10, 4.17, 4.23, 4.32, 4.35, 4.42, 4.50, 4.57, 4.67, 4.70, 4.79
- Self linking number
- 0