| Min(phi) over symmetries of the knot is: [-3,-1,0,1,1,2,1,1,2,3,2,0,1,2,1,1,0,2,0,0,0] |
| Flat knots (up to 7 crossings) with same phi are :['6.1314'] |
| 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+44t^5+123t^3+9t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1314'] |
| 2-strand cable arrow polynomial of the knot is: -256*K1**4*K2**2 + 480*K1**4*K2 - 672*K1**4 + 32*K1**3*K2*K3 - 96*K1**3*K3 - 1024*K1**2*K2**4 + 2656*K1**2*K2**3 - 6464*K1**2*K2**2 - 576*K1**2*K2*K4 + 4928*K1**2*K2 - 256*K1**2*K3**2 - 2952*K1**2 + 1408*K1*K2**3*K3 - 1248*K1*K2**2*K3 - 320*K1*K2**2*K5 - 64*K1*K2*K3*K4 + 4968*K1*K2*K3 + 800*K1*K3*K4 + 56*K1*K4*K5 - 1944*K2**4 - 544*K2**2*K3**2 - 8*K2**2*K4**2 + 1608*K2**2*K4 - 1518*K2**2 + 344*K2*K3*K5 + 8*K2*K4*K6 - 1120*K3**2 - 498*K4**2 - 80*K5**2 - 2*K6**2 + 2352 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1314'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.73980', 'vk6.73985', 'vk6.74499', 'vk6.74508', 'vk6.75955', 'vk6.75966', 'vk6.76711', 'vk6.76720', 'vk6.78951', 'vk6.78954', 'vk6.79500', 'vk6.79503', 'vk6.80481', 'vk6.80484', 'vk6.80955', 'vk6.80958', 'vk6.83010', 'vk6.83098', 'vk6.83654', 'vk6.83786', 'vk6.83945', 'vk6.84118', 'vk6.84265', 'vk6.85179', 'vk6.85544', 'vk6.85870', 'vk6.86260', 'vk6.86584', 'vk6.86740', 'vk6.87450', 'vk6.88310', 'vk6.89743'] |
| 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 | O1O2O3U4O5O6U1U2O4U6U5U3 |
| R3 orbit | {'O1O2O3U4O5O6U1U2O4U6U5U3'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3U1U4U5O6U2U3O5O4U6 |
| Gauss code of K* | O1O2O3U4U5U3O6U2U1O4O5U6 |
| Gauss code of -K* | O1O2O3U4O5O6U3U2O4U1U5U6 |
| 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 2 0 1 1],[ 3 0 1 3 2 2 1],[ 1 -1 0 2 1 1 0],[-2 -3 -2 0 0 -1 -1],[ 0 -2 -1 0 0 0 1],[-1 -2 -1 1 0 0 0],[-1 -1 0 1 -1 0 0]] |
| Primitive based matrix | [[ 0 2 1 1 0 -1 -3],[-2 0 -1 -1 0 -2 -3],[-1 1 0 0 0 -1 -2],[-1 1 0 0 -1 0 -1],[ 0 0 0 1 0 -1 -2],[ 1 2 1 0 1 0 -1],[ 3 3 2 1 2 1 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-2,-1,-1,0,1,3,1,1,0,2,3,0,0,1,2,1,0,1,1,2,1] |
| Phi over symmetry | [-3,-1,0,1,1,2,1,1,2,3,2,0,1,2,1,1,0,2,0,0,0] |
| Phi of -K | [-3,-1,0,1,1,2,1,1,2,3,2,0,1,2,1,1,0,2,0,0,0] |
| Phi of K* | [-2,-1,-1,0,1,3,0,0,2,1,2,0,0,2,3,1,1,2,0,1,1] |
| Phi of -K* | [-3,-1,0,1,1,2,1,2,1,2,3,1,0,1,2,1,0,0,0,1,1] |
| Symmetry type of based matrix | c |
| u-polynomial | t^3-t^2-t |
| Normalized Jones-Krushkal polynomial | 7z^2+24z+21 |
| Enhanced Jones-Krushkal polynomial | -2w^4z^2+9w^3z^2-2w^3z+26w^2z+21w |
| Inner characteristic polynomial | t^6+28t^4+54t^2+1 |
| Outer characteristic polynomial | t^7+44t^5+123t^3+9t |
| 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 - 672*K1**4 + 32*K1**3*K2*K3 - 96*K1**3*K3 - 1024*K1**2*K2**4 + 2656*K1**2*K2**3 - 6464*K1**2*K2**2 - 576*K1**2*K2*K4 + 4928*K1**2*K2 - 256*K1**2*K3**2 - 2952*K1**2 + 1408*K1*K2**3*K3 - 1248*K1*K2**2*K3 - 320*K1*K2**2*K5 - 64*K1*K2*K3*K4 + 4968*K1*K2*K3 + 800*K1*K3*K4 + 56*K1*K4*K5 - 1944*K2**4 - 544*K2**2*K3**2 - 8*K2**2*K4**2 + 1608*K2**2*K4 - 1518*K2**2 + 344*K2*K3*K5 + 8*K2*K4*K6 - 1120*K3**2 - 498*K4**2 - 80*K5**2 - 2*K6**2 + 2352 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{1, 6}, {4, 5}, {2, 3}], [{4, 6}, {3, 5}, {1, 2}]] |
| If K is slice | False |