| Min(phi) over symmetries of the knot is: [-2,-1,0,0,1,2,0,0,1,2,3,-1,-1,1,2,-1,0,0,1,1,1] |
| Flat knots (up to 7 crossings) with same phi are :['6.1275'] |
| Arrow polynomial of the knot is: 4*K1**3 - 4*K1**2 - 4*K1*K2 - K1 + 2*K2 + K3 + 3 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['6.209', '6.231', '6.391', '6.419', '6.600', '6.661', '6.744', '6.812', '6.826', '6.1114', '6.1125', '6.1202', '6.1275', '6.1292', '6.1305', '6.1322', '6.1365', '6.1481', '6.1483', '6.1497', '6.1543', '6.1549', '6.1572', '6.1577', '6.1580', '6.1594', '6.1641', '6.1658', '6.1683', '6.1753', '6.1830', '6.1907', '6.1928'] |
| Outer characteristic polynomial of the knot is: t^7+35t^5+65t^3+5t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1275'] |
| 2-strand cable arrow polynomial of the knot is: -128*K1**4*K2**2 + 256*K1**4*K2 - 880*K1**4 + 352*K1**3*K2*K3 - 224*K1**3*K3 + 416*K1**2*K2**3 - 2400*K1**2*K2**2 - 96*K1**2*K2*K4 + 5192*K1**2*K2 - 304*K1**2*K3**2 - 4404*K1**2 + 96*K1*K2**3*K3 - 960*K1*K2**2*K3 - 64*K1*K2**2*K5 + 3800*K1*K2*K3 + 992*K1*K3*K4 - 32*K2**6 + 96*K2**4*K4 - 624*K2**4 - 32*K2**3*K6 - 240*K2**2*K3**2 - 112*K2**2*K4**2 + 1096*K2**2*K4 - 3222*K2**2 - 96*K2*K3**2*K4 + 248*K2*K3*K5 + 112*K2*K4*K6 + 24*K3**2*K6 - 1520*K3**2 - 620*K4**2 - 60*K5**2 - 18*K6**2 + 3354 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1275'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.11283', 'vk6.11363', 'vk6.12544', 'vk6.12657', 'vk6.18361', 'vk6.18700', 'vk6.24805', 'vk6.25264', 'vk6.30965', 'vk6.31092', 'vk6.32143', 'vk6.32264', 'vk6.36987', 'vk6.37440', 'vk6.44168', 'vk6.44488', 'vk6.52035', 'vk6.52124', 'vk6.52878', 'vk6.52945', 'vk6.56144', 'vk6.56372', 'vk6.60666', 'vk6.61013', 'vk6.63656', 'vk6.63703', 'vk6.64084', 'vk6.64131', 'vk6.65801', 'vk6.66056', 'vk6.68798', 'vk6.69007'] |
| 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 | O1O2O3U1O4O5U3U5O6U4U2U6 |
| R3 orbit | {'O1O2O3U1O4O5U3U5O6U4U2U6'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3U4U2U5O4U6U1O6O5U3 |
| Gauss code of K* | O1O2O3U4U2U5O4U1U6O5O6U3 |
| Gauss code of -K* | O1O2O3U1O4O5U4U3O6U5U2U6 |
| 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 -2 0 -1 0 1 2],[ 2 0 2 1 1 1 1],[ 0 -2 0 -2 1 1 2],[ 1 -1 2 0 2 1 1],[ 0 -1 -1 -2 0 0 1],[-1 -1 -1 -1 0 0 0],[-2 -1 -2 -1 -1 0 0]] |
| Primitive based matrix | [[ 0 2 1 0 0 -1 -2],[-2 0 0 -1 -2 -1 -1],[-1 0 0 0 -1 -1 -1],[ 0 1 0 0 -1 -2 -1],[ 0 2 1 1 0 -2 -2],[ 1 1 1 2 2 0 -1],[ 2 1 1 1 2 1 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-2,-1,0,0,1,2,0,1,2,1,1,0,1,1,1,1,2,1,2,2,1] |
| Phi over symmetry | [-2,-1,0,0,1,2,0,0,1,2,3,-1,-1,1,2,-1,0,0,1,1,1] |
| Phi of -K | [-2,-1,0,0,1,2,0,0,1,2,3,-1,-1,1,2,-1,0,0,1,1,1] |
| Phi of K* | [-2,-1,0,0,1,2,1,0,1,2,3,0,1,1,2,1,-1,0,-1,1,0] |
| Phi of -K* | [-2,-1,0,0,1,2,1,1,2,1,1,2,2,1,1,-1,0,1,1,2,0] |
| Symmetry type of based matrix | c |
| u-polynomial | 0 |
| Normalized Jones-Krushkal polynomial | 4z^2+23z+31 |
| Enhanced Jones-Krushkal polynomial | 4w^3z^2+23w^2z+31w |
| Inner characteristic polynomial | t^6+25t^4+19t^2 |
| Outer characteristic polynomial | t^7+35t^5+65t^3+5t |
| Flat arrow polynomial | 4*K1**3 - 4*K1**2 - 4*K1*K2 - K1 + 2*K2 + K3 + 3 |
| 2-strand cable arrow polynomial | -128*K1**4*K2**2 + 256*K1**4*K2 - 880*K1**4 + 352*K1**3*K2*K3 - 224*K1**3*K3 + 416*K1**2*K2**3 - 2400*K1**2*K2**2 - 96*K1**2*K2*K4 + 5192*K1**2*K2 - 304*K1**2*K3**2 - 4404*K1**2 + 96*K1*K2**3*K3 - 960*K1*K2**2*K3 - 64*K1*K2**2*K5 + 3800*K1*K2*K3 + 992*K1*K3*K4 - 32*K2**6 + 96*K2**4*K4 - 624*K2**4 - 32*K2**3*K6 - 240*K2**2*K3**2 - 112*K2**2*K4**2 + 1096*K2**2*K4 - 3222*K2**2 - 96*K2*K3**2*K4 + 248*K2*K3*K5 + 112*K2*K4*K6 + 24*K3**2*K6 - 1520*K3**2 - 620*K4**2 - 60*K5**2 - 18*K6**2 + 3354 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{1, 6}, {3, 5}, {2, 4}]] |
| If K is slice | False |