| Min(phi) over symmetries of the knot is: [-3,-1,0,0,1,3,-1,2,3,1,4,1,1,1,1,0,0,1,0,2,0] |
| Flat knots (up to 7 crossings) with same phi are :['6.430'] |
| Arrow polynomial of the knot is: 4*K1**3 - 4*K1*K2 - K1 + K3 + 1 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['6.395', '6.430', '6.440', '6.548', '6.551', '6.774', '6.832', '6.887', '6.908', '6.911', '6.1205', '6.1332', '6.1339', '6.1341', '6.1346', '6.1382', '6.1488', '6.1651', '6.1655', '6.1686'] |
| Outer characteristic polynomial of the knot is: t^7+64t^5+107t^3+10t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.430'] |
| 2-strand cable arrow polynomial of the knot is: 768*K1**4*K2 - 1952*K1**4 + 832*K1**3*K2*K3 - 544*K1**3*K3 - 128*K1**2*K2**4 + 384*K1**2*K2**3 + 128*K1**2*K2**2*K4 - 3840*K1**2*K2**2 + 256*K1**2*K2*K3**2 - 384*K1**2*K2*K4 + 6048*K1**2*K2 - 1824*K1**2*K3**2 - 32*K1**2*K3*K5 - 32*K1**2*K4**2 - 3872*K1**2 + 320*K1*K2**3*K3 - 1728*K1*K2**2*K3 - 128*K1*K2**2*K5 - 448*K1*K2*K3*K4 + 6224*K1*K2*K3 - 32*K1*K2*K4*K5 + 2000*K1*K3*K4 + 96*K1*K4*K5 + 16*K1*K5*K6 - 32*K2**6 + 32*K2**4*K4 - 560*K2**4 - 736*K2**2*K3**2 - 16*K2**2*K4**2 + 1048*K2**2*K4 - 3222*K2**2 + 640*K2*K3*K5 + 24*K2*K4*K6 - 1928*K3**2 - 544*K4**2 - 104*K5**2 - 10*K6**2 + 3278 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.430'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.20146', 'vk6.20148', 'vk6.20156', 'vk6.20170', 'vk6.21438', 'vk6.21444', 'vk6.27262', 'vk6.27268', 'vk6.27284', 'vk6.27294', 'vk6.28924', 'vk6.28930', 'vk6.28946', 'vk6.38681', 'vk6.38691', 'vk6.38705', 'vk6.38727', 'vk6.40885', 'vk6.40907', 'vk6.47267', 'vk6.47280', 'vk6.47294', 'vk6.56971', 'vk6.56981', 'vk6.56992', 'vk6.57004', 'vk6.58125', 'vk6.62672', 'vk6.62688', 'vk6.67466', 'vk6.70032', 'vk6.70050'] |
| The R3 orbit of minmal crossing diagrams contains: |
| The diagrammatic symmetry type of this knot is c. |
| The reverse -K is |
| The mirror image K* is |
| The reversed mirror image -K* is |
| The fillings (up to the first 10) associated to the algebraic genus: |
| Or click here to check the fillings |
| invariant | value |
|---|---|
| Gauss code | O1O2O3O4O5U6U1O6U4U3U5U2 |
| R3 orbit | {'O1O2O3O4O5U6U1O6U4U3U5U2'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3O4O5U4U1U3U2O6U5U6 |
| Gauss code of K* | O1O2O3O4U5U4U2U1U3O6O5U6 |
| Gauss code of -K* | O1O2O3O4U5O6O5U2U4U3U1U6 |
| Diagrammatic symmetry type | c |
| Flat genus of the diagram | 3 |
| If K is checkerboard colorable | False |
| If K is almost classical | False |
| Based matrix from Gauss code | [[ 0 -3 1 0 0 3 -1],[ 3 0 3 1 0 2 3],[-1 -3 0 -1 -1 2 -1],[ 0 -1 1 0 0 2 0],[ 0 0 1 0 0 1 0],[-3 -2 -2 -2 -1 0 -3],[ 1 -3 1 0 0 3 0]] |
| Primitive based matrix | [[ 0 3 1 0 0 -1 -3],[-3 0 -2 -1 -2 -3 -2],[-1 2 0 -1 -1 -1 -3],[ 0 1 1 0 0 0 0],[ 0 2 1 0 0 0 -1],[ 1 3 1 0 0 0 -3],[ 3 2 3 0 1 3 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-3,-1,0,0,1,3,2,1,2,3,2,1,1,1,3,0,0,0,0,1,3] |
| Phi over symmetry | [-3,-1,0,0,1,3,-1,2,3,1,4,1,1,1,1,0,0,1,0,2,0] |
| Phi of -K | [-3,-1,0,0,1,3,-1,2,3,1,4,1,1,1,1,0,0,1,0,2,0] |
| Phi of K* | [-3,-1,0,0,1,3,0,1,2,1,4,0,0,1,1,0,1,2,1,3,-1] |
| Phi of -K* | [-3,-1,0,0,1,3,3,0,1,3,2,0,0,1,3,0,1,1,1,2,2] |
| Symmetry type of based matrix | c |
| u-polynomial | 0 |
| Normalized Jones-Krushkal polynomial | 7z^2+26z+25 |
| Enhanced Jones-Krushkal polynomial | 7w^3z^2-2w^3z+28w^2z+25w |
| Inner characteristic polynomial | t^6+44t^4+45t^2+1 |
| Outer characteristic polynomial | t^7+64t^5+107t^3+10t |
| Flat arrow polynomial | 4*K1**3 - 4*K1*K2 - K1 + K3 + 1 |
| 2-strand cable arrow polynomial | 768*K1**4*K2 - 1952*K1**4 + 832*K1**3*K2*K3 - 544*K1**3*K3 - 128*K1**2*K2**4 + 384*K1**2*K2**3 + 128*K1**2*K2**2*K4 - 3840*K1**2*K2**2 + 256*K1**2*K2*K3**2 - 384*K1**2*K2*K4 + 6048*K1**2*K2 - 1824*K1**2*K3**2 - 32*K1**2*K3*K5 - 32*K1**2*K4**2 - 3872*K1**2 + 320*K1*K2**3*K3 - 1728*K1*K2**2*K3 - 128*K1*K2**2*K5 - 448*K1*K2*K3*K4 + 6224*K1*K2*K3 - 32*K1*K2*K4*K5 + 2000*K1*K3*K4 + 96*K1*K4*K5 + 16*K1*K5*K6 - 32*K2**6 + 32*K2**4*K4 - 560*K2**4 - 736*K2**2*K3**2 - 16*K2**2*K4**2 + 1048*K2**2*K4 - 3222*K2**2 + 640*K2*K3*K5 + 24*K2*K4*K6 - 1928*K3**2 - 544*K4**2 - 104*K5**2 - 10*K6**2 + 3278 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{2, 6}, {1, 5}, {3, 4}], [{2, 6}, {1, 5}, {4}, {3}]] |
| If K is slice | False |