| Min(phi) over symmetries of the knot is: [-3,-2,0,1,2,2,-1,2,4,2,3,1,2,1,1,1,1,2,2,2,0] |
| Flat knots (up to 7 crossings) with same phi are :['6.734'] |
| Arrow polynomial of the knot is: -2*K1**2 - 2*K1*K2 + K1 + K2 + K3 + 2 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['6.217', '6.219', '6.304', '6.349', '6.390', '6.400', '6.416', '6.515', '6.518', '6.530', '6.582', '6.616', '6.629', '6.641', '6.645', '6.702', '6.710', '6.715', '6.729', '6.733', '6.734', '6.802', '6.840', '6.845', '6.854', '6.860', '6.900', '6.905', '6.921', '6.924', '6.979', '6.980', '6.996', '6.1044', '6.1067', '6.1086', '6.1100', '6.1139', '6.1145', '6.1149', '6.1167', '6.1169', '6.1183', '6.1314'] |
| Outer characteristic polynomial of the knot is: t^7+63t^5+65t^3+5t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.734'] |
| 2-strand cable arrow polynomial of the knot is: -256*K1**4*K2**2 + 480*K1**4*K2 - 912*K1**4 + 480*K1**3*K2*K3 - 1056*K1**3*K3 + 288*K1**2*K2**3 - 2016*K1**2*K2**2 - 192*K1**2*K2*K4 + 4480*K1**2*K2 - 336*K1**2*K3**2 - 96*K1**2*K3*K5 - 3572*K1**2 + 64*K1*K2**3*K3 - 320*K1*K2**2*K3 - 32*K1*K2*K3*K4 + 3568*K1*K2*K3 + 528*K1*K3*K4 + 144*K1*K4*K5 - 232*K2**4 - 80*K2**2*K3**2 - 8*K2**2*K4**2 + 352*K2**2*K4 - 2286*K2**2 + 128*K2*K3*K5 + 8*K2*K4*K6 - 1200*K3**2 - 274*K4**2 - 92*K5**2 - 2*K6**2 + 2440 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.734'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.4669', 'vk6.4958', 'vk6.6131', 'vk6.6620', 'vk6.8140', 'vk6.8544', 'vk6.9518', 'vk6.9875', 'vk6.20367', 'vk6.21708', 'vk6.27671', 'vk6.29215', 'vk6.39107', 'vk6.41361', 'vk6.45859', 'vk6.47520', 'vk6.48701', 'vk6.48906', 'vk6.49465', 'vk6.49686', 'vk6.50721', 'vk6.50922', 'vk6.51200', 'vk6.51403', 'vk6.57236', 'vk6.58461', 'vk6.61854', 'vk6.62989', 'vk6.66851', 'vk6.67719', 'vk6.69483', 'vk6.70205'] |
| 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 | O1O2O3O4U1O5U6U5U2O6U4U3 |
| R3 orbit | {'O1O2O3O4U1O5U6U5U2O6U4U3'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3O4U2U1O5U3U6U5O6U4 |
| Gauss code of K* | O1O2O3U1O4O5U6U3U5U4O6U2 |
| Gauss code of -K* | O1O2O3U2O4U5U6U1U4O6O5U3 |
| 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 0 2 2 1 -2],[ 3 0 1 3 2 0 2],[ 0 -1 0 1 0 0 -1],[-2 -3 -1 0 0 1 -3],[-2 -2 0 0 0 1 -3],[-1 0 0 -1 -1 0 -1],[ 2 -2 1 3 3 1 0]] |
| Primitive based matrix | [[ 0 2 2 1 0 -2 -3],[-2 0 0 1 0 -3 -2],[-2 0 0 1 -1 -3 -3],[-1 -1 -1 0 0 -1 0],[ 0 0 1 0 0 -1 -1],[ 2 3 3 1 1 0 -2],[ 3 2 3 0 1 2 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-2,-2,-1,0,2,3,0,-1,0,3,2,-1,1,3,3,0,1,0,1,1,2] |
| Phi over symmetry | [-3,-2,0,1,2,2,-1,2,4,2,3,1,2,1,1,1,1,2,2,2,0] |
| Phi of -K | [-3,-2,0,1,2,2,-1,2,4,2,3,1,2,1,1,1,1,2,2,2,0] |
| Phi of K* | [-2,-2,-1,0,2,3,0,2,1,1,2,2,2,1,3,1,2,4,1,2,-1] |
| Phi of -K* | [-3,-2,0,1,2,2,2,1,0,2,3,1,1,3,3,0,0,1,-1,-1,0] |
| Symmetry type of based matrix | c |
| u-polynomial | t^3-t^2-t |
| Normalized Jones-Krushkal polynomial | 5z^2+22z+25 |
| Enhanced Jones-Krushkal polynomial | 5w^3z^2+22w^2z+25w |
| Inner characteristic polynomial | t^6+41t^4+38t^2+1 |
| Outer characteristic polynomial | t^7+63t^5+65t^3+5t |
| Flat arrow polynomial | -2*K1**2 - 2*K1*K2 + K1 + K2 + K3 + 2 |
| 2-strand cable arrow polynomial | -256*K1**4*K2**2 + 480*K1**4*K2 - 912*K1**4 + 480*K1**3*K2*K3 - 1056*K1**3*K3 + 288*K1**2*K2**3 - 2016*K1**2*K2**2 - 192*K1**2*K2*K4 + 4480*K1**2*K2 - 336*K1**2*K3**2 - 96*K1**2*K3*K5 - 3572*K1**2 + 64*K1*K2**3*K3 - 320*K1*K2**2*K3 - 32*K1*K2*K3*K4 + 3568*K1*K2*K3 + 528*K1*K3*K4 + 144*K1*K4*K5 - 232*K2**4 - 80*K2**2*K3**2 - 8*K2**2*K4**2 + 352*K2**2*K4 - 2286*K2**2 + 128*K2*K3*K5 + 8*K2*K4*K6 - 1200*K3**2 - 274*K4**2 - 92*K5**2 - 2*K6**2 + 2440 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{2, 6}, {1, 5}, {3, 4}], [{3, 6}, {1, 5}, {2, 4}], [{3, 6}, {2, 5}, {1, 4}], [{3, 6}, {4, 5}, {1, 2}]] |
| If K is slice | False |