| Min(phi) over symmetries of the knot is: [-3,-2,0,1,1,3,-1,1,1,2,5,1,0,0,2,0,0,1,0,0,0] |
| Flat knots (up to 7 crossings) with same phi are :['6.891'] |
| Arrow polynomial of the knot is: -2*K1**2 - 4*K1*K2 + 2*K1 + K2 + 2*K3 + 2 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['6.120', '6.213', '6.216', '6.320', '6.322', '6.615', '6.617', '6.891', '6.951', '6.955', '6.1001', '6.1012', '6.1022', '6.1043', '6.1047', '6.1063', '6.1074', '6.1249', '6.1544', '6.1546', '6.1555', '6.1573', '6.1574', '6.1585', '6.1756', '6.1757', '6.1762', '6.1802', '6.1803', '6.1824', '6.1881', '6.1935'] |
| Outer characteristic polynomial of the knot is: t^7+62t^5+67t^3+7t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.891'] |
| 2-strand cable arrow polynomial of the knot is: -1280*K1**2*K2**4 - 512*K1**2*K2**3*K4 + 2080*K1**2*K2**3 - 4336*K1**2*K2**2 - 544*K1**2*K2*K4 + 3632*K1**2*K2 - 16*K1**2*K3**2 - 3260*K1**2 + 1920*K1*K2**3*K3 + 576*K1*K2**2*K3*K4 - 1056*K1*K2**2*K3 - 96*K1*K2**2*K5 - 128*K1*K2*K3*K4 - 32*K1*K2*K3*K6 + 4136*K1*K2*K3 - 32*K1*K2*K4*K5 + 784*K1*K3*K4 + 48*K1*K4*K5 + 56*K1*K5*K6 - 128*K2**6 + 448*K2**4*K4 - 1672*K2**4 - 800*K2**2*K3**2 - 464*K2**2*K4**2 + 1632*K2**2*K4 - 1840*K2**2 + 296*K2*K3*K5 + 144*K2*K4*K6 - 16*K3**4 + 24*K3**2*K6 - 1348*K3**2 - 710*K4**2 - 96*K5**2 - 64*K6**2 + 2652 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.891'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.11553', 'vk6.11892', 'vk6.12909', 'vk6.13209', 'vk6.20682', 'vk6.22120', 'vk6.28194', 'vk6.29617', 'vk6.31333', 'vk6.31742', 'vk6.32503', 'vk6.32906', 'vk6.39648', 'vk6.41887', 'vk6.46244', 'vk6.47849', 'vk6.52331', 'vk6.52594', 'vk6.53181', 'vk6.53471', 'vk6.57614', 'vk6.58772', 'vk6.62282', 'vk6.63218', 'vk6.63829', 'vk6.63964', 'vk6.64276', 'vk6.64470', 'vk6.67078', 'vk6.67942', 'vk6.69689', 'vk6.70370'] |
| 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 | O1O2O3O4U2U3O5O6U1U6U5U4 |
| R3 orbit | {'O1O2O3O4U2U3O5O6U1U6U5U4'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3O4U1U5U6U4O6O5U2U3 |
| Gauss code of K* | O1O2O3O4U1U5U6U4O5O6U3U2 |
| Gauss code of -K* | O1O2O3O4U3U2O5O6U1U5U6U4 |
| 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 -2 0 3 1 1],[ 3 0 -1 1 5 2 1],[ 2 1 0 1 2 0 0],[ 0 -1 -1 0 1 0 0],[-3 -5 -2 -1 0 0 0],[-1 -2 0 0 0 0 0],[-1 -1 0 0 0 0 0]] |
| Primitive based matrix | [[ 0 3 1 1 0 -2 -3],[-3 0 0 0 -1 -2 -5],[-1 0 0 0 0 0 -1],[-1 0 0 0 0 0 -2],[ 0 1 0 0 0 -1 -1],[ 2 2 0 0 1 0 1],[ 3 5 1 2 1 -1 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-3,-1,-1,0,2,3,0,0,1,2,5,0,0,0,1,0,0,2,1,1,-1] |
| Phi over symmetry | [-3,-2,0,1,1,3,-1,1,1,2,5,1,0,0,2,0,0,1,0,0,0] |
| Phi of -K | [-3,-2,0,1,1,3,2,2,2,3,1,1,3,3,3,1,1,2,0,2,2] |
| Phi of K* | [-3,-1,-1,0,2,3,2,2,2,3,1,0,1,3,2,1,3,3,1,2,2] |
| Phi of -K* | [-3,-2,0,1,1,3,-1,1,1,2,5,1,0,0,2,0,0,1,0,0,0] |
| Symmetry type of based matrix | c |
| u-polynomial | t^2-2t |
| Normalized Jones-Krushkal polynomial | 5z^2+18z+17 |
| Enhanced Jones-Krushkal polynomial | -4w^4z^2+9w^3z^2-4w^3z+22w^2z+17w |
| Inner characteristic polynomial | t^6+38t^4+34t^2 |
| Outer characteristic polynomial | t^7+62t^5+67t^3+7t |
| Flat arrow polynomial | -2*K1**2 - 4*K1*K2 + 2*K1 + K2 + 2*K3 + 2 |
| 2-strand cable arrow polynomial | -1280*K1**2*K2**4 - 512*K1**2*K2**3*K4 + 2080*K1**2*K2**3 - 4336*K1**2*K2**2 - 544*K1**2*K2*K4 + 3632*K1**2*K2 - 16*K1**2*K3**2 - 3260*K1**2 + 1920*K1*K2**3*K3 + 576*K1*K2**2*K3*K4 - 1056*K1*K2**2*K3 - 96*K1*K2**2*K5 - 128*K1*K2*K3*K4 - 32*K1*K2*K3*K6 + 4136*K1*K2*K3 - 32*K1*K2*K4*K5 + 784*K1*K3*K4 + 48*K1*K4*K5 + 56*K1*K5*K6 - 128*K2**6 + 448*K2**4*K4 - 1672*K2**4 - 800*K2**2*K3**2 - 464*K2**2*K4**2 + 1632*K2**2*K4 - 1840*K2**2 + 296*K2*K3*K5 + 144*K2*K4*K6 - 16*K3**4 + 24*K3**2*K6 - 1348*K3**2 - 710*K4**2 - 96*K5**2 - 64*K6**2 + 2652 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{2, 6}, {1, 5}, {3, 4}], [{2, 6}, {3, 5}, {1, 4}], [{3, 6}, {2, 5}, {1, 4}], [{5, 6}, {1, 4}, {2, 3}]] |
| If K is slice | False |