| Min(phi) over symmetries of the knot is: [-4,-1,-1,3,3,1,2,3,4,0,1,2,2,3,0] |
| Flat knots (up to 7 crossings) with same phi are :['5.4'] |
| Arrow polynomial of the knot is: 2*K2**2 - K4 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['5.4', '5.12', '7.339', '7.372', '7.683', '7.686', '7.783', '7.835', '7.1400', '7.1509', '7.2242', '7.2291', '7.2585', '7.2587', '7.2589', '7.2606', '7.2607', '7.2776', '7.2941', '7.2953', '7.2956', '7.2957', '7.3001', '7.3005', '7.3308', '7.3356', '7.3463', '7.3497', '7.4355', '7.4630', '7.6229', '7.6235', '7.6242', '7.6283', '7.6342', '7.6479', '7.6854', '7.6912', '7.7078', '7.7178', '7.8229', '7.9338', '7.9346', '7.9415', '7.9424', '7.9478', '7.9487', '7.9524', '7.9549', '7.9674', '7.9728', '7.9827', '7.9931', '7.9936', '7.9941', '7.10092', '7.11563', '7.11618', '7.11635', '7.11705', '7.12038', '7.12304', '7.12350', '7.13109', '7.13121', '7.13180', '7.13218', '7.13238', '7.13252', '7.13426', '7.13553', '7.14151', '7.14201', '7.14879', '7.15006', '7.15093', '7.15121', '7.15135', '7.15143', '7.17076'] |
| Outer characteristic polynomial of the knot is: t^6+84t^4+47t^2 |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['5.4'] |
| 2-strand cable arrow polynomial of the knot is: -256*K1**2*K3**2 - 272*K1**2 + 160*K1*K2*K3 + 576*K1*K3*K4 + 48*K1*K4*K5 + 16*K1*K6*K7 - 24*K2**2 + 16*K2*K3*K5 - 256*K3**2 + 16*K3*K4*K7 - 8*K4**4 + 8*K4**2*K8 - 256*K4**2 - 32*K5**2 - 8*K6**2 - 16*K7**2 - 2*K8**2 + 288 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['5.4'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk5.2194', 'vk5.2196', 'vk5.2209', 'vk5.2210', 'vk5.2211', 'vk5.2244', 'vk5.2248', 'vk5.2250', 'vk5.2380', 'vk5.2424'] |
| 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 | O1O2O3O4O5U1U3U2U5U4 |
| R3 orbit | {'O1O2O3O4O5U1U3U2U5U4'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3O4O5U2U1U4U3U5 |
| Gauss code of K* | Same |
| Gauss code of -K* | O1O2O3O4O5U2U1U4U3U5 |
| Diagrammatic symmetry type | + |
| 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 -1 -1 3 3],[ 4 0 2 1 4 3],[ 1 -2 0 0 3 2],[ 1 -1 0 0 2 1],[-3 -4 -3 -2 0 0],[-3 -3 -2 -1 0 0]] |
| Primitive based matrix | [[ 0 3 3 -1 -1 -4],[-3 0 0 -1 -2 -3],[-3 0 0 -2 -3 -4],[ 1 1 2 0 0 -1],[ 1 2 3 0 0 -2],[ 4 3 4 1 2 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-3,-3,1,1,4,0,1,2,3,2,3,4,0,1,2] |
| Phi over symmetry | [-4,-1,-1,3,3,1,2,3,4,0,1,2,2,3,0] |
| Phi of -K | [-4,-1,-1,3,3,1,2,3,4,0,1,2,2,3,0] |
| Phi of K* | [-3,-3,1,1,4,0,1,2,3,2,3,4,0,1,2] |
| Phi of -K* | [-4,-1,-1,3,3,1,2,3,4,0,1,2,2,3,0] |
| Symmetry type of based matrix | + |
| u-polynomial | t^4-2t^3+2t |
| Normalized Jones-Krushkal polynomial | -5z-9 |
| Enhanced Jones-Krushkal polynomial | -4w^4z+4w^3z-5w^2z-9w |
| Inner characteristic polynomial | t^5+48t^3+7t |
| Outer characteristic polynomial | t^6+84t^4+47t^2 |
| Flat arrow polynomial | 2*K2**2 - K4 |
| 2-strand cable arrow polynomial | -256*K1**2*K3**2 - 272*K1**2 + 160*K1*K2*K3 + 576*K1*K3*K4 + 48*K1*K4*K5 + 16*K1*K6*K7 - 24*K2**2 + 16*K2*K3*K5 - 256*K3**2 + 16*K3*K4*K7 - 8*K4**4 + 8*K4**2*K8 - 256*K4**2 - 32*K5**2 - 8*K6**2 - 16*K7**2 - 2*K8**2 + 288 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{4, 5}, {2, 3}, {1}]] |
| If K is slice | False |