| Min(phi) over symmetries of the knot is: [-4,0,0,2,2,1,3,2,4,1,1,1,1,1,-1] |
| Flat knots (up to 7 crossings) with same phi are :['5.9'] |
| Arrow polynomial of the knot is: 8*K1**4 - 4*K1**2*K2 - 4*K1**2 + 1 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['5.9', '7.378', '7.925', '7.1773', '7.2266', '7.2859', '7.2873', '7.3320', '7.4764', '7.5374', '7.5556', '7.6318', '7.6647', '7.6737', '7.7228', '7.7231', '7.7583', '7.7769', '7.8121', '7.9277', '7.9299', '7.9319', '7.12484', '7.13399', '7.14738', '7.15188', '7.16409', '7.16419', '7.16430', '7.16585', '7.16591', '7.17482', '7.17488', '7.17510', '7.17540', '7.31327', '7.31341'] |
| Outer characteristic polynomial of the knot is: t^6+60t^4+47t^2 |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['5.9', '7.3332'] |
| 2-strand cable arrow polynomial of the knot is: -128*K2**8 + 128*K2**6*K4 - 256*K2**6 - 32*K2**4*K4**2 + 256*K2**4*K4 - 640*K2**4 - 96*K2**2*K4**2 + 480*K2**2*K4 + 272*K2**2 + 16*K2*K4*K6 - 64*K4**2 + 62 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['5.9'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk5.1950', 'vk5.1954', 'vk5.1958', 'vk5.1961', 'vk5.1965', 'vk5.1968', 'vk5.1970', 'vk5.2078', 'vk5.2158', 'vk5.2431'] |
| The R3 orbit of minmal crossing diagrams contains: |
| The diagrammatic symmetry type of this knot is +. |
| The reverse -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 | O1O2O3O4O5U1U4U5U2U3 |
| R3 orbit | {'O1O2O3O4O5U1U4U5U2U3'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3O4O5U3U4U1U2U5 |
| Gauss code of K* | Same |
| Gauss code of -K* | O1O2O3O4O5U3U4U1U2U5 |
| Diagrammatic symmetry type | + |
| Flat genus of the diagram | 2 |
| If K is checkerboard colorable | True |
| If K is almost classical | False |
| Based matrix from Gauss code | [[ 0 -4 0 2 0 2],[ 4 0 3 4 1 2],[ 0 -3 0 1 -1 1],[-2 -4 -1 0 -1 1],[ 0 -1 1 1 0 1],[-2 -2 -1 -1 -1 0]] |
| Primitive based matrix | [[ 0 2 2 0 0 -4],[-2 0 1 -1 -1 -4],[-2 -1 0 -1 -1 -2],[ 0 1 1 0 1 -1],[ 0 1 1 -1 0 -3],[ 4 4 2 1 3 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-2,-2,0,0,4,-1,1,1,4,1,1,2,-1,1,3] |
| Phi over symmetry | [-4,0,0,2,2,1,3,2,4,1,1,1,1,1,-1] |
| Phi of -K | [-4,0,0,2,2,1,3,2,4,1,1,1,1,1,-1] |
| Phi of K* | [-2,-2,0,0,4,-1,1,1,4,1,1,2,-1,1,3] |
| Phi of -K* | [-4,0,0,2,2,1,3,2,4,1,1,1,1,1,-1] |
| Symmetry type of based matrix | + |
| u-polynomial | t^4-2t^2 |
| Normalized Jones-Krushkal polynomial | -3z^2-10z-7 |
| Enhanced Jones-Krushkal polynomial | 2w^4z^2-5w^3z^2-10w^2z-7 |
| Inner characteristic polynomial | t^5+36t^3+7t |
| Outer characteristic polynomial | t^6+60t^4+47t^2 |
| Flat arrow polynomial | 8*K1**4 - 4*K1**2*K2 - 4*K1**2 + 1 |
| 2-strand cable arrow polynomial | -128*K2**8 + 128*K2**6*K4 - 256*K2**6 - 32*K2**4*K4**2 + 256*K2**4*K4 - 640*K2**4 - 96*K2**2*K4**2 + 480*K2**2*K4 + 272*K2**2 + 16*K2*K4*K6 - 64*K4**2 + 62 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{1, 5}, {2, 4}, {3}], [{3, 5}, {2, 4}, {1}], [{5}, {2, 4}, {1, 3}], [{5}, {2, 4}, {3}, {1}]] |
| If K is slice | False |