| Min(phi) over symmetries of the knot is: [-3,-1,0,0,1,3,-1,1,2,2,4,0,2,0,1,1,0,1,0,2,1] |
| Flat knots (up to 7 crossings) with same phi are :['6.838'] |
| Arrow polynomial of the knot is: 8*K1**3 - 4*K1**2 - 4*K1*K2 - 4*K1 + 2*K2 + 3 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['6.206', '6.236', '6.575', '6.580', '6.613', '6.619', '6.810', '6.819', '6.831', '6.838', '6.957', '6.1018', '6.1028', '6.1046', '6.1073', '6.1279', '6.1507', '6.1532', '6.1556', '6.1639', '6.1688', '6.1924', '6.1931'] |
| Outer characteristic polynomial of the knot is: t^7+66t^5+95t^3+7t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.838'] |
| 2-strand cable arrow polynomial of the knot is: -448*K1**4 - 768*K1**2*K2**4 + 1728*K1**2*K2**3 - 5008*K1**2*K2**2 - 256*K1**2*K2*K4 + 4880*K1**2*K2 - 3672*K1**2 + 1824*K1*K2**3*K3 - 1024*K1*K2**2*K3 - 256*K1*K2**2*K5 - 96*K1*K2*K3*K4 + 4768*K1*K2*K3 + 392*K1*K3*K4 + 8*K1*K4*K5 - 768*K2**6 + 768*K2**4*K4 - 2576*K2**4 - 1232*K2**2*K3**2 - 352*K2**2*K4**2 + 1992*K2**2*K4 - 1608*K2**2 + 512*K2*K3*K5 + 160*K2*K4*K6 - 1308*K3**2 - 492*K4**2 - 44*K5**2 - 40*K6**2 + 2914 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.838'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.71619', 'vk6.71779', 'vk6.72200', 'vk6.72348', 'vk6.73371', 'vk6.73532', 'vk6.75276', 'vk6.75542', 'vk6.77237', 'vk6.77316', 'vk6.77566', 'vk6.77678', 'vk6.78263', 'vk6.78512', 'vk6.80079', 'vk6.80227', 'vk6.81111', 'vk6.81177', 'vk6.81198', 'vk6.81236', 'vk6.81323', 'vk6.81511', 'vk6.82012', 'vk6.82431', 'vk6.82744', 'vk6.85461', 'vk6.86350', 'vk6.86916', 'vk6.87126', 'vk6.88089', 'vk6.88664', 'vk6.88770'] |
| 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 | O1O2O3O4U1U2O5O6U4U5U3U6 |
| R3 orbit | {'O1O2O3O4U1U2O5O6U4U5U3U6'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3O4U5U2U6U1O5O6U3U4 |
| Gauss code of K* | O1O2O3O4U5U6U3U1O5O6U2U4 |
| Gauss code of -K* | O1O2O3O4U1U3O5O6U4U2U5U6 |
| 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 1 0 0 3],[ 3 0 1 3 2 1 2],[ 1 -1 0 2 1 1 2],[-1 -3 -2 0 -1 1 3],[ 0 -2 -1 1 0 1 2],[ 0 -1 -1 -1 -1 0 1],[-3 -2 -2 -3 -2 -1 0]] |
| Primitive based matrix | [[ 0 3 1 0 0 -1 -3],[-3 0 -3 -1 -2 -2 -2],[-1 3 0 1 -1 -2 -3],[ 0 1 -1 0 -1 -1 -1],[ 0 2 1 1 0 -1 -2],[ 1 2 2 1 1 0 -1],[ 3 2 3 1 2 1 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-3,-1,0,0,1,3,3,1,2,2,2,-1,1,2,3,1,1,1,1,2,1] |
| Phi over symmetry | [-3,-1,0,0,1,3,-1,1,2,2,4,0,2,0,1,1,0,1,0,2,1] |
| Phi of -K | [-3,-1,0,0,1,3,1,1,2,1,4,0,0,0,2,-1,0,1,2,2,-1] |
| Phi of K* | [-3,-1,0,0,1,3,-1,1,2,2,4,0,2,0,1,1,0,1,0,2,1] |
| Phi of -K* | [-3,-1,0,0,1,3,1,1,2,3,2,1,1,2,2,-1,-1,1,1,2,3] |
| Symmetry type of based matrix | c |
| u-polynomial | 0 |
| Normalized Jones-Krushkal polynomial | 4z^2+17z+19 |
| Enhanced Jones-Krushkal polynomial | -4w^4z^2+8w^3z^2-4w^3z+21w^2z+19w |
| Inner characteristic polynomial | t^6+46t^4+17t^2 |
| Outer characteristic polynomial | t^7+66t^5+95t^3+7t |
| Flat arrow polynomial | 8*K1**3 - 4*K1**2 - 4*K1*K2 - 4*K1 + 2*K2 + 3 |
| 2-strand cable arrow polynomial | -448*K1**4 - 768*K1**2*K2**4 + 1728*K1**2*K2**3 - 5008*K1**2*K2**2 - 256*K1**2*K2*K4 + 4880*K1**2*K2 - 3672*K1**2 + 1824*K1*K2**3*K3 - 1024*K1*K2**2*K3 - 256*K1*K2**2*K5 - 96*K1*K2*K3*K4 + 4768*K1*K2*K3 + 392*K1*K3*K4 + 8*K1*K4*K5 - 768*K2**6 + 768*K2**4*K4 - 2576*K2**4 - 1232*K2**2*K3**2 - 352*K2**2*K4**2 + 1992*K2**2*K4 - 1608*K2**2 + 512*K2*K3*K5 + 160*K2*K4*K6 - 1308*K3**2 - 492*K4**2 - 44*K5**2 - 40*K6**2 + 2914 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{1, 6}, {4, 5}, {2, 3}]] |
| If K is slice | False |