| Min(phi) over symmetries of the knot is: [-3,-2,0,1,2,2,0,1,2,2,4,1,1,1,2,0,0,0,1,0,-2] |
| Flat knots (up to 7 crossings) with same phi are :['6.573'] |
| Arrow polynomial of the knot is: 4*K1**3 - 6*K1**2 - 2*K1*K2 - 2*K1 + 3*K2 + 4 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['6.573', '6.628', '6.703', '6.704', '6.723', '6.796', '6.1083', '6.1099', '6.1315'] |
| Outer characteristic polynomial of the knot is: t^7+73t^5+46t^3 |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.573'] |
| 2-strand cable arrow polynomial of the knot is: -64*K1**4*K2**2 + 160*K1**4*K2 - 480*K1**4 + 32*K1**3*K2*K3 + 224*K1**2*K2**3 - 1184*K1**2*K2**2 + 1568*K1**2*K2 - 128*K1**2*K3**2 - 16*K1**2*K4**2 - 1144*K1**2 + 96*K1*K2**3*K3 + 1232*K1*K2*K3 + 168*K1*K3*K4 + 24*K1*K4*K5 - 32*K2**6 + 32*K2**4*K4 - 328*K2**4 - 96*K2**2*K3**2 - 8*K2**2*K4**2 + 192*K2**2*K4 - 704*K2**2 + 32*K2*K3*K5 - 412*K3**2 - 110*K4**2 - 12*K5**2 + 956 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.573'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.71342', 'vk6.71393', 'vk6.71419', 'vk6.71856', 'vk6.71882', 'vk6.71919', 'vk6.71941', 'vk6.74198', 'vk6.74322', 'vk6.74343', 'vk6.74967', 'vk6.74987', 'vk6.75613', 'vk6.75806', 'vk6.76371', 'vk6.76534', 'vk6.76558', 'vk6.76941', 'vk6.76995', 'vk6.77017', 'vk6.77072', 'vk6.78596', 'vk6.78797', 'vk6.79233', 'vk6.79368', 'vk6.79792', 'vk6.79812', 'vk6.80242', 'vk6.80719', 'vk6.80844', 'vk6.81282', 'vk6.81486', 'vk6.84053', 'vk6.86016', 'vk6.87067', 'vk6.87077', 'vk6.87749', 'vk6.88050', 'vk6.88212', 'vk6.89402'] |
| 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 | O1O2O3O4U1O5U2O6U4U5U6U3 |
| R3 orbit | {'O1O2O3O4U1O5U2U3O6U5U4U6', 'O1O2O3O4U1O5U2O6U4U5U6U3'} |
| R3 orbit length | 2 |
| Gauss code of -K | O1O2O3O4U2U5U6U1O5U3O6U4 |
| Gauss code of K* | O1O2O3O4U5U6U4U1O5U2O6U3 |
| Gauss code of -K* | O1O2O3O4U2O5U3O6U4U1U5U6 |
| Diagrammatic symmetry type | c |
| Flat genus of the diagram | 2 |
| If K is checkerboard colorable | False |
| If K is almost classical | False |
| Based matrix from Gauss code | [[ 0 -3 -2 2 0 1 2],[ 3 0 1 3 2 2 1],[ 2 -1 0 3 1 2 2],[-2 -3 -3 0 -2 0 2],[ 0 -2 -1 2 0 1 2],[-1 -2 -2 0 -1 0 1],[-2 -1 -2 -2 -2 -1 0]] |
| Primitive based matrix | [[ 0 2 2 1 0 -2 -3],[-2 0 2 0 -2 -3 -3],[-2 -2 0 -1 -2 -2 -1],[-1 0 1 0 -1 -2 -2],[ 0 2 2 1 0 -1 -2],[ 2 3 2 2 1 0 -1],[ 3 3 1 2 2 1 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-2,-2,-1,0,2,3,-2,0,2,3,3,1,2,2,1,1,2,2,1,2,1] |
| Phi over symmetry | [-3,-2,0,1,2,2,0,1,2,2,4,1,1,1,2,0,0,0,1,0,-2] |
| Phi of -K | [-3,-2,0,1,2,2,0,1,2,2,4,1,1,1,2,0,0,0,1,0,-2] |
| Phi of K* | [-2,-2,-1,0,2,3,-2,0,0,2,4,1,0,1,2,0,1,2,1,1,0] |
| Phi of -K* | [-3,-2,0,1,2,2,1,2,2,1,3,1,2,2,3,1,2,2,1,0,-2] |
| Symmetry type of based matrix | c |
| u-polynomial | t^3-t^2-t |
| Normalized Jones-Krushkal polynomial | 9z+19 |
| Enhanced Jones-Krushkal polynomial | -2w^3z+11w^2z+19w |
| Inner characteristic polynomial | t^6+51t^4+11t^2 |
| Outer characteristic polynomial | t^7+73t^5+46t^3 |
| Flat arrow polynomial | 4*K1**3 - 6*K1**2 - 2*K1*K2 - 2*K1 + 3*K2 + 4 |
| 2-strand cable arrow polynomial | -64*K1**4*K2**2 + 160*K1**4*K2 - 480*K1**4 + 32*K1**3*K2*K3 + 224*K1**2*K2**3 - 1184*K1**2*K2**2 + 1568*K1**2*K2 - 128*K1**2*K3**2 - 16*K1**2*K4**2 - 1144*K1**2 + 96*K1*K2**3*K3 + 1232*K1*K2*K3 + 168*K1*K3*K4 + 24*K1*K4*K5 - 32*K2**6 + 32*K2**4*K4 - 328*K2**4 - 96*K2**2*K3**2 - 8*K2**2*K4**2 + 192*K2**2*K4 - 704*K2**2 + 32*K2*K3*K5 - 412*K3**2 - 110*K4**2 - 12*K5**2 + 956 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{4, 6}, {2, 5}, {1, 3}], [{4, 6}, {2, 5}, {3}, {1}]] |
| If K is slice | False |