| Min(phi) over symmetries of the knot is: [-3,-1,0,0,2,2,0,1,3,2,3,1,2,1,1,0,1,1,2,2,-1] |
| Flat knots (up to 7 crossings) with same phi are :['6.1349'] |
| Arrow polynomial of the knot is: -8*K1**2 - 2*K1*K2 + K1 + 4*K2 + K3 + 5 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['6.377', '6.638', '6.646', '6.647', '6.657', '6.658', '6.662', '6.692', '6.695', '6.714', '6.720', '6.726', '6.730', '6.731', '6.749', '6.756', '6.772', '6.779', '6.781', '6.800', '6.829', '6.1085', '6.1089', '6.1302', '6.1349', '6.1350', '6.1360', '6.1362', '6.1375', '6.1384'] |
| Outer characteristic polynomial of the knot is: t^7+59t^5+53t^3+5t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1349'] |
| 2-strand cable arrow polynomial of the knot is: -64*K1**4*K2**2 + 192*K1**4*K2 - 1936*K1**4 + 64*K1**3*K2*K3 + 64*K1**3*K3*K4 - 448*K1**3*K3 + 96*K1**2*K2**3 - 2544*K1**2*K2**2 - 224*K1**2*K2*K4 + 6280*K1**2*K2 - 592*K1**2*K3**2 - 32*K1**2*K3*K5 - 96*K1**2*K4**2 - 4428*K1**2 - 160*K1*K2**2*K3 - 96*K1*K2*K3*K4 + 4136*K1*K2*K3 + 1144*K1*K3*K4 + 128*K1*K4*K5 - 96*K2**4 - 8*K2**2*K4**2 + 424*K2**2*K4 - 3238*K2**2 + 64*K2*K3*K5 + 8*K2*K4*K6 - 1500*K3**2 - 532*K4**2 - 48*K5**2 - 2*K6**2 + 3442 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1349'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.71387', 'vk6.71448', 'vk6.71909', 'vk6.71970', 'vk6.72451', 'vk6.72611', 'vk6.72730', 'vk6.72808', 'vk6.72873', 'vk6.73039', 'vk6.74221', 'vk6.74360', 'vk6.74428', 'vk6.74850', 'vk6.75042', 'vk6.76613', 'vk6.76901', 'vk6.77052', 'vk6.77418', 'vk6.77751', 'vk6.77804', 'vk6.79271', 'vk6.79406', 'vk6.79745', 'vk6.79822', 'vk6.79885', 'vk6.80856', 'vk6.80910', 'vk6.81375', 'vk6.85515', 'vk6.87200', 'vk6.89271'] |
| 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 | O1O2O3U1O4O5U6U3U4O6U2U5 |
| R3 orbit | {'O1O2O3U1O4O5U6U3U4O6U2U5'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3U4U2O5U6U1U5O4O6U3 |
| Gauss code of K* | O1O2O3U1O4O5U6U4U2O6U3U5 |
| Gauss code of -K* | O1O2O3U4U1O5U2U6U5O4O6U3 |
| 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 0 1 3 -2],[ 2 0 2 1 1 2 1],[ 0 -2 0 0 2 3 -2],[ 0 -1 0 0 1 1 -1],[-1 -1 -2 -1 0 0 -1],[-3 -2 -3 -1 0 0 -3],[ 2 -1 2 1 1 3 0]] |
| Primitive based matrix | [[ 0 3 1 0 0 -2 -2],[-3 0 0 -1 -3 -2 -3],[-1 0 0 -1 -2 -1 -1],[ 0 1 1 0 0 -1 -1],[ 0 3 2 0 0 -2 -2],[ 2 2 1 1 2 0 1],[ 2 3 1 1 2 -1 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-3,-1,0,0,2,2,0,1,3,2,3,1,2,1,1,0,1,1,2,2,-1] |
| Phi over symmetry | [-3,-1,0,0,2,2,0,1,3,2,3,1,2,1,1,0,1,1,2,2,-1] |
| Phi of -K | [-2,-2,0,0,1,3,-1,0,1,2,3,0,1,2,2,0,-1,0,0,2,2] |
| Phi of K* | [-3,-1,0,0,2,2,2,0,2,2,3,-1,0,2,2,0,0,0,1,1,-1] |
| Phi of -K* | [-2,-2,0,0,1,3,-1,1,2,1,3,1,2,1,2,0,1,1,2,3,0] |
| Symmetry type of based matrix | c |
| u-polynomial | -t^3+2t^2-t |
| Normalized Jones-Krushkal polynomial | 2z^2+19z+31 |
| Enhanced Jones-Krushkal polynomial | 2w^3z^2+19w^2z+31w |
| Inner characteristic polynomial | t^6+41t^4+25t^2+1 |
| Outer characteristic polynomial | t^7+59t^5+53t^3+5t |
| Flat arrow polynomial | -8*K1**2 - 2*K1*K2 + K1 + 4*K2 + K3 + 5 |
| 2-strand cable arrow polynomial | -64*K1**4*K2**2 + 192*K1**4*K2 - 1936*K1**4 + 64*K1**3*K2*K3 + 64*K1**3*K3*K4 - 448*K1**3*K3 + 96*K1**2*K2**3 - 2544*K1**2*K2**2 - 224*K1**2*K2*K4 + 6280*K1**2*K2 - 592*K1**2*K3**2 - 32*K1**2*K3*K5 - 96*K1**2*K4**2 - 4428*K1**2 - 160*K1*K2**2*K3 - 96*K1*K2*K3*K4 + 4136*K1*K2*K3 + 1144*K1*K3*K4 + 128*K1*K4*K5 - 96*K2**4 - 8*K2**2*K4**2 + 424*K2**2*K4 - 3238*K2**2 + 64*K2*K3*K5 + 8*K2*K4*K6 - 1500*K3**2 - 532*K4**2 - 48*K5**2 - 2*K6**2 + 3442 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{2, 6}, {4, 5}, {1, 3}], [{2, 6}, {4, 5}, {3}, {1}]] |
| If K is slice | False |