| Min(phi) over symmetries of the knot is: [-2,0,0,0,1,1,0,0,1,1,2,-1,0,-1,1,0,0,1,1,0,0] |
| Flat knots (up to 7 crossings) with same phi are :['6.1869'] |
| Arrow polynomial of the knot is: 4*K1**3 - 10*K1**2 - 4*K1*K2 - K1 + 5*K2 + K3 + 6 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['6.241', '6.341', '6.542', '6.567', '6.699', '6.713', '6.771', '6.791', '6.1025', '6.1039', '6.1041', '6.1072', '6.1077', '6.1121', '6.1123', '6.1499', '6.1502', '6.1531', '6.1645', '6.1648', '6.1726', '6.1727', '6.1761', '6.1784', '6.1807', '6.1823', '6.1832', '6.1869', '6.1873', '6.1874'] |
| Outer characteristic polynomial of the knot is: t^7+17t^5+54t^3+6t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1869'] |
| 2-strand cable arrow polynomial of the knot is: -128*K1**4*K2**2 + 352*K1**4*K2 - 2096*K1**4 + 224*K1**3*K2*K3 - 704*K1**3*K3 + 384*K1**2*K2**3 - 4528*K1**2*K2**2 - 416*K1**2*K2*K4 + 8680*K1**2*K2 - 368*K1**2*K3**2 - 16*K1**2*K4**2 - 5812*K1**2 + 128*K1*K2**3*K3 - 384*K1*K2**2*K3 - 192*K1*K2*K3*K4 + 5736*K1*K2*K3 + 744*K1*K3*K4 + 64*K1*K4*K5 - 32*K2**6 + 64*K2**4*K4 - 600*K2**4 - 160*K2**2*K3**2 - 48*K2**2*K4**2 + 824*K2**2*K4 - 4014*K2**2 + 176*K2*K3*K5 + 16*K2*K4*K6 - 1640*K3**2 - 406*K4**2 - 44*K5**2 - 2*K6**2 + 4196 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1869'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.71349', 'vk6.71399', 'vk6.71415', 'vk6.71864', 'vk6.71878', 'vk6.71925', 'vk6.71937', 'vk6.74321', 'vk6.74327', 'vk6.74968', 'vk6.74974', 'vk6.76533', 'vk6.76543', 'vk6.76942', 'vk6.77003', 'vk6.77021', 'vk6.77062', 'vk6.77076', 'vk6.77392', 'vk6.79367', 'vk6.79793', 'vk6.79799', 'vk6.80826', 'vk6.80833', 'vk6.81276', 'vk6.81474', 'vk6.81476', 'vk6.83839', 'vk6.87059', 'vk6.87073', 'vk6.88039', 'vk6.89557'] |
| 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 | O1O2O3U4U1O5U2O6O4U5U6U3 |
| R3 orbit | {'O1O2O3U4U1O5U2O6O4U5U6U3'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3U1U4U5O6O4U2O5U3U6 |
| Gauss code of K* | O1O2O3U4U5U3O6O4U1O5U2U6 |
| Gauss code of -K* | O1O2O3U4U2O5U3O6O4U1U5U6 |
| 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 -1 0 2 0 -1 0],[ 1 0 1 1 0 0 -1],[ 0 -1 0 1 0 0 0],[-2 -1 -1 0 0 -2 0],[ 0 0 0 0 0 -1 -1],[ 1 0 0 2 1 0 1],[ 0 1 0 0 1 -1 0]] |
| Primitive based matrix | [[ 0 2 0 0 0 -1 -1],[-2 0 0 0 -1 -1 -2],[ 0 0 0 1 0 1 -1],[ 0 0 -1 0 0 0 -1],[ 0 1 0 0 0 -1 0],[ 1 1 -1 0 1 0 0],[ 1 2 1 1 0 0 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-2,0,0,0,1,1,0,0,1,1,2,-1,0,-1,1,0,0,1,1,0,0] |
| Phi over symmetry | [-2,0,0,0,1,1,0,0,1,1,2,-1,0,-1,1,0,0,1,1,0,0] |
| Phi of -K | [-1,-1,0,0,0,2,0,0,0,1,1,1,2,0,2,1,0,2,0,2,1] |
| Phi of K* | [-2,0,0,0,1,1,1,2,2,1,2,0,0,1,0,-1,0,1,0,2,0] |
| Phi of -K* | [-1,-1,0,0,0,2,0,-1,0,1,1,1,1,0,2,1,0,0,0,0,1] |
| Symmetry type of based matrix | c |
| u-polynomial | -t^2+2t |
| Normalized Jones-Krushkal polynomial | 3z^2+22z+33 |
| Enhanced Jones-Krushkal polynomial | 3w^3z^2+22w^2z+33w |
| Inner characteristic polynomial | t^6+11t^4+27t^2+1 |
| Outer characteristic polynomial | t^7+17t^5+54t^3+6t |
| Flat arrow polynomial | 4*K1**3 - 10*K1**2 - 4*K1*K2 - K1 + 5*K2 + K3 + 6 |
| 2-strand cable arrow polynomial | -128*K1**4*K2**2 + 352*K1**4*K2 - 2096*K1**4 + 224*K1**3*K2*K3 - 704*K1**3*K3 + 384*K1**2*K2**3 - 4528*K1**2*K2**2 - 416*K1**2*K2*K4 + 8680*K1**2*K2 - 368*K1**2*K3**2 - 16*K1**2*K4**2 - 5812*K1**2 + 128*K1*K2**3*K3 - 384*K1*K2**2*K3 - 192*K1*K2*K3*K4 + 5736*K1*K2*K3 + 744*K1*K3*K4 + 64*K1*K4*K5 - 32*K2**6 + 64*K2**4*K4 - 600*K2**4 - 160*K2**2*K3**2 - 48*K2**2*K4**2 + 824*K2**2*K4 - 4014*K2**2 + 176*K2*K3*K5 + 16*K2*K4*K6 - 1640*K3**2 - 406*K4**2 - 44*K5**2 - 2*K6**2 + 4196 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{1, 6}, {4, 5}, {2, 3}]] |
| If K is slice | False |