| Min(phi) over symmetries of the knot is: [-3,-1,0,1,1,2,1,1,3,3,2,0,1,1,1,-1,0,0,0,2,2] |
| Flat knots (up to 7 crossings) with same phi are :['6.840'] |
| 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+50t^5+53t^3+7t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.840'] |
| 2-strand cable arrow polynomial of the knot is: -1024*K1**2*K2**4 + 2784*K1**2*K2**3 - 5056*K1**2*K2**2 - 800*K1**2*K2*K4 + 3216*K1**2*K2 - 2552*K1**2 + 1600*K1*K2**3*K3 - 640*K1*K2**2*K3 - 416*K1*K2**2*K5 - 160*K1*K2*K3*K4 + 3656*K1*K2*K3 + 384*K1*K3*K4 + 184*K1*K4*K5 - 128*K2**6 + 192*K2**4*K4 - 2296*K2**4 - 32*K2**3*K6 - 672*K2**2*K3**2 - 72*K2**2*K4**2 + 1584*K2**2*K4 - 798*K2**2 + 568*K2*K3*K5 + 24*K2*K4*K6 - 872*K3**2 - 418*K4**2 - 200*K5**2 - 2*K6**2 + 1944 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.840'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.17024', 'vk6.17265', 'vk6.20568', 'vk6.21975', 'vk6.23447', 'vk6.23744', 'vk6.28032', 'vk6.29490', 'vk6.35523', 'vk6.35969', 'vk6.39435', 'vk6.41633', 'vk6.42939', 'vk6.43232', 'vk6.46021', 'vk6.47689', 'vk6.55206', 'vk6.55440', 'vk6.57439', 'vk6.58609', 'vk6.59601', 'vk6.59920', 'vk6.62113', 'vk6.63082', 'vk6.65011', 'vk6.65215', 'vk6.66972', 'vk6.67834', 'vk6.68286', 'vk6.68437', 'vk6.69588', 'vk6.70281'] |
| 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 | O1O2O3O4U1U2O5O6U4U6U5U3 |
| R3 orbit | {'O1O2O3O4U1U2O5O6U4U6U5U3'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3O4U2U5U6U1O6O5U3U4 |
| Gauss code of K* | O1O2O3O4U5U6U4U1O5O6U3U2 |
| Gauss code of -K* | O1O2O3O4U3U2O5O6U4U1U5U6 |
| 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 1 1],[ 1 -1 0 2 1 1 1],[-2 -3 -2 0 -2 1 1],[ 0 -2 -1 2 0 2 1],[-1 -1 -1 -1 -2 0 0],[-1 -1 -1 -1 -1 0 0]] |
| Primitive based matrix | [[ 0 2 1 1 0 -1 -3],[-2 0 1 1 -2 -2 -3],[-1 -1 0 0 -1 -1 -1],[-1 -1 0 0 -2 -1 -1],[ 0 2 1 2 0 -1 -2],[ 1 2 1 1 1 0 -1],[ 3 3 1 1 2 1 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-2,-1,-1,0,1,3,-1,-1,2,2,3,0,1,1,1,2,1,1,1,2,1] |
| Phi over symmetry | [-3,-1,0,1,1,2,1,1,3,3,2,0,1,1,1,-1,0,0,0,2,2] |
| Phi of -K | [-3,-1,0,1,1,2,1,1,3,3,2,0,1,1,1,-1,0,0,0,2,2] |
| Phi of K* | [-2,-1,-1,0,1,3,2,2,0,1,2,0,-1,1,3,0,1,3,0,1,1] |
| Phi of -K* | [-3,-1,0,1,1,2,1,2,1,1,3,1,1,1,2,1,2,2,0,-1,-1] |
| Symmetry type of based matrix | c |
| u-polynomial | t^3-t^2-t |
| Normalized Jones-Krushkal polynomial | 6z^2+19z+15 |
| Enhanced Jones-Krushkal polynomial | -4w^4z^2+10w^3z^2-4w^3z+23w^2z+15w |
| Inner characteristic polynomial | t^6+34t^4+12t^2 |
| Outer characteristic polynomial | t^7+50t^5+53t^3+7t |
| Flat arrow polynomial | -2*K1**2 - 2*K1*K2 + K1 + K2 + K3 + 2 |
| 2-strand cable arrow polynomial | -1024*K1**2*K2**4 + 2784*K1**2*K2**3 - 5056*K1**2*K2**2 - 800*K1**2*K2*K4 + 3216*K1**2*K2 - 2552*K1**2 + 1600*K1*K2**3*K3 - 640*K1*K2**2*K3 - 416*K1*K2**2*K5 - 160*K1*K2*K3*K4 + 3656*K1*K2*K3 + 384*K1*K3*K4 + 184*K1*K4*K5 - 128*K2**6 + 192*K2**4*K4 - 2296*K2**4 - 32*K2**3*K6 - 672*K2**2*K3**2 - 72*K2**2*K4**2 + 1584*K2**2*K4 - 798*K2**2 + 568*K2*K3*K5 + 24*K2*K4*K6 - 872*K3**2 - 418*K4**2 - 200*K5**2 - 2*K6**2 + 1944 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{2, 6}, {1, 5}, {3, 4}], [{2, 6}, {3, 5}, {1, 4}], [{2, 6}, {4, 5}, {1, 3}], [{3, 6}, {4, 5}, {1, 2}]] |
| If K is slice | False |