| Min(phi) over symmetries of the knot is: [-4,-2,0,1,2,3,0,3,1,3,5,1,0,1,2,0,1,2,0,0,0] |
| Flat knots (up to 7 crossings) with same phi are :['6.228'] |
| Arrow polynomial of the knot is: -2*K1**2 - 2*K1*K2 - 2*K1*K3 + K1 + 2*K2 + K3 + K4 + 2 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['6.62', '6.176', '6.181', '6.194', '6.228', '6.267', '6.268', '6.449'] |
| Outer characteristic polynomial of the knot is: t^7+89t^5+64t^3 |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.228'] |
| 2-strand cable arrow polynomial of the knot is: -64*K1**6 + 64*K1**4*K2 - 480*K1**4 - 240*K1**2*K2**2 + 712*K1**2*K2 - 368*K1**2*K3**2 - 48*K1**2*K4**2 - 632*K1**2 + 64*K1*K2*K3**3 + 1080*K1*K2*K3 + 32*K1*K3**3*K4 + 472*K1*K3*K4 + 56*K1*K4*K5 + 16*K1*K5*K6 - 24*K2**4 - 192*K2**2*K3**2 - 8*K2**2*K4**2 + 80*K2**2*K4 - 8*K2**2*K6**2 - 638*K2**2 + 136*K2*K3*K5 + 32*K2*K4*K6 + 8*K2*K6*K8 - 80*K3**4 - 32*K3**2*K4**2 + 40*K3**2*K6 - 492*K3**2 + 8*K3*K4*K7 - 200*K4**2 - 52*K5**2 - 34*K6**2 - 2*K8**2 + 792 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.228'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.16581', 'vk6.16674', 'vk6.18131', 'vk6.18465', 'vk6.22980', 'vk6.23101', 'vk6.24586', 'vk6.24997', 'vk6.34973', 'vk6.35094', 'vk6.35396', 'vk6.35817', 'vk6.36721', 'vk6.37138', 'vk6.39406', 'vk6.41597', 'vk6.42542', 'vk6.42653', 'vk6.42869', 'vk6.43148', 'vk6.43989', 'vk6.44299', 'vk6.45982', 'vk6.47656', 'vk6.54812', 'vk6.55364', 'vk6.56243', 'vk6.57404', 'vk6.59240', 'vk6.59801', 'vk6.60843', 'vk6.62071', 'vk6.64786', 'vk6.64851', 'vk6.65602', 'vk6.65907', 'vk6.68084', 'vk6.68149', 'vk6.68673', 'vk6.68882'] |
| 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 | O1O2O3O4O5U3O6U1U6U5U2U4 |
| R3 orbit | {'O1O2O3O4O5U3O6U1U6U5U2U4', 'O1O2O3O4U2O5O6U1U6U3U5U4'} |
| R3 orbit length | 2 |
| Gauss code of -K | O1O2O3O4O5U2U4U1U6U5O6U3 |
| Gauss code of K* | O1O2O3O4O5U1U4U6U5U3O6U2 |
| Gauss code of -K* | O1O2O3O4O5U4O6U3U1U6U2U5 |
| Diagrammatic symmetry type | c |
| Flat genus of the diagram | 2 |
| If K is checkerboard colorable | False |
| If K is almost classical | False |
| Based matrix from Gauss code | [[ 0 -4 0 -2 3 2 1],[ 4 0 3 0 5 3 1],[ 0 -3 0 -1 2 1 0],[ 2 0 1 0 2 1 0],[-3 -5 -2 -2 0 0 0],[-2 -3 -1 -1 0 0 0],[-1 -1 0 0 0 0 0]] |
| Primitive based matrix | [[ 0 3 2 1 0 -2 -4],[-3 0 0 0 -2 -2 -5],[-2 0 0 0 -1 -1 -3],[-1 0 0 0 0 0 -1],[ 0 2 1 0 0 -1 -3],[ 2 2 1 0 1 0 0],[ 4 5 3 1 3 0 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-3,-2,-1,0,2,4,0,0,2,2,5,0,1,1,3,0,0,1,1,3,0] |
| Phi over symmetry | [-4,-2,0,1,2,3,0,3,1,3,5,1,0,1,2,0,1,2,0,0,0] |
| Phi of -K | [-4,-2,0,1,2,3,2,1,4,3,2,1,3,3,3,1,1,1,1,2,1] |
| Phi of K* | [-3,-2,-1,0,2,4,1,2,1,3,2,1,1,3,3,1,3,4,1,1,2] |
| Phi of -K* | [-4,-2,0,1,2,3,0,3,1,3,5,1,0,1,2,0,1,2,0,0,0] |
| Symmetry type of based matrix | c |
| u-polynomial | t^4-t^3-t |
| Normalized Jones-Krushkal polynomial | 9z+19 |
| Enhanced Jones-Krushkal polynomial | 9w^2z+19w |
| Inner characteristic polynomial | t^6+55t^4+14t^2 |
| Outer characteristic polynomial | t^7+89t^5+64t^3 |
| Flat arrow polynomial | -2*K1**2 - 2*K1*K2 - 2*K1*K3 + K1 + 2*K2 + K3 + K4 + 2 |
| 2-strand cable arrow polynomial | -64*K1**6 + 64*K1**4*K2 - 480*K1**4 - 240*K1**2*K2**2 + 712*K1**2*K2 - 368*K1**2*K3**2 - 48*K1**2*K4**2 - 632*K1**2 + 64*K1*K2*K3**3 + 1080*K1*K2*K3 + 32*K1*K3**3*K4 + 472*K1*K3*K4 + 56*K1*K4*K5 + 16*K1*K5*K6 - 24*K2**4 - 192*K2**2*K3**2 - 8*K2**2*K4**2 + 80*K2**2*K4 - 8*K2**2*K6**2 - 638*K2**2 + 136*K2*K3*K5 + 32*K2*K4*K6 + 8*K2*K6*K8 - 80*K3**4 - 32*K3**2*K4**2 + 40*K3**2*K6 - 492*K3**2 + 8*K3*K4*K7 - 200*K4**2 - 52*K5**2 - 34*K6**2 - 2*K8**2 + 792 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{3, 6}, {2, 5}, {1, 4}], [{3, 6}, {2, 5}, {4}, {1}]] |
| If K is slice | False |