| Min(phi) over symmetries of the knot is: [-3,-1,0,1,1,2,1,0,2,3,2,-1,0,1,1,0,0,0,0,0,1] |
| Flat knots (up to 7 crossings) with same phi are :['6.1100'] |
| 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+60t^5+60t^3+8t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1100'] |
| 2-strand cable arrow polynomial of the knot is: -16*K1**4 - 928*K1**3*K3 - 384*K1**2*K2**2 + 128*K1**2*K2*K3**2 + 3192*K1**2*K2 - 656*K1**2*K3**2 - 4012*K1**2 + 160*K1*K2**3*K3 - 256*K1*K2**2*K3 - 416*K1*K2*K3*K4 + 4168*K1*K2*K3 + 752*K1*K3*K4 + 56*K1*K4*K5 - 200*K2**4 - 400*K2**2*K3**2 - 8*K2**2*K4**2 + 464*K2**2*K4 - 2670*K2**2 + 352*K2*K3*K5 + 8*K2*K4*K6 - 1704*K3**2 - 306*K4**2 - 36*K5**2 - 2*K6**2 + 2712 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1100'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.73740', 'vk6.73859', 'vk6.74204', 'vk6.74828', 'vk6.75653', 'vk6.75859', 'vk6.76385', 'vk6.76882', 'vk6.78664', 'vk6.78855', 'vk6.79240', 'vk6.79722', 'vk6.80284', 'vk6.80414', 'vk6.80731', 'vk6.81080', 'vk6.81625', 'vk6.81812', 'vk6.81997', 'vk6.82323', 'vk6.82369', 'vk6.82724', 'vk6.83217', 'vk6.84245', 'vk6.84328', 'vk6.84423', 'vk6.84507', 'vk6.85667', 'vk6.86550', 'vk6.87554', 'vk6.88281', 'vk6.89411'] |
| 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 | O1O2O3O4U1U5O6U4U3O5U2U6 |
| R3 orbit | {'O1O2O3O4U1U5O6U4U3O5U2U6'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3O4U5U3O6U2U1O5U6U4 |
| Gauss code of K* | O1O2U3O4O5U2O6O3U1U6U5U4 |
| Gauss code of -K* | O1O2U3O4O5U1O3O6U5U4U2U6 |
| 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 0 1 1 -1 2],[ 3 0 3 2 1 1 3],[ 0 -3 0 1 1 -2 2],[-1 -2 -1 0 0 -2 1],[-1 -1 -1 0 0 -1 0],[ 1 -1 2 2 1 0 2],[-2 -3 -2 -1 0 -2 0]] |
| Primitive based matrix | [[ 0 2 1 1 0 -1 -3],[-2 0 0 -1 -2 -2 -3],[-1 0 0 0 -1 -1 -1],[-1 1 0 0 -1 -2 -2],[ 0 2 1 1 0 -2 -3],[ 1 2 1 2 2 0 -1],[ 3 3 1 2 3 1 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-2,-1,-1,0,1,3,0,1,2,2,3,0,1,1,1,1,2,2,2,3,1] |
| Phi over symmetry | [-3,-1,0,1,1,2,1,0,2,3,2,-1,0,1,1,0,0,0,0,0,1] |
| Phi of -K | [-3,-1,0,1,1,2,1,0,2,3,2,-1,0,1,1,0,0,0,0,0,1] |
| Phi of K* | [-2,-1,-1,0,1,3,0,1,0,1,2,0,0,0,2,0,1,3,-1,0,1] |
| Phi of -K* | [-3,-1,0,1,1,2,1,3,1,2,3,2,1,2,2,1,1,2,0,0,1] |
| Symmetry type of based matrix | c |
| u-polynomial | t^3-t^2-t |
| Normalized Jones-Krushkal polynomial | 3z^2+16z+21 |
| Enhanced Jones-Krushkal polynomial | -2w^4z^2+5w^3z^2-6w^3z+22w^2z+21w |
| Inner characteristic polynomial | t^6+44t^4+25t^2+1 |
| Outer characteristic polynomial | t^7+60t^5+60t^3+8t |
| Flat arrow polynomial | -2*K1**2 - 2*K1*K2 + K1 + K2 + K3 + 2 |
| 2-strand cable arrow polynomial | -16*K1**4 - 928*K1**3*K3 - 384*K1**2*K2**2 + 128*K1**2*K2*K3**2 + 3192*K1**2*K2 - 656*K1**2*K3**2 - 4012*K1**2 + 160*K1*K2**3*K3 - 256*K1*K2**2*K3 - 416*K1*K2*K3*K4 + 4168*K1*K2*K3 + 752*K1*K3*K4 + 56*K1*K4*K5 - 200*K2**4 - 400*K2**2*K3**2 - 8*K2**2*K4**2 + 464*K2**2*K4 - 2670*K2**2 + 352*K2*K3*K5 + 8*K2*K4*K6 - 1704*K3**2 - 306*K4**2 - 36*K5**2 - 2*K6**2 + 2712 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{3, 6}, {1, 5}, {2, 4}]] |
| If K is slice | False |