| Min(phi) over symmetries of the knot is: [-4,1,1,1,1,1,2,3,4,0,0,0,0,0,0] |
| Flat knots (up to 7 crossings) with same phi are :['5.12'] |
| 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+50t^4+20t^2 |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['5.12'] |
| 2-strand cable arrow polynomial of the knot is: -128*K1**2 + 160*K1*K3*K4 + 96*K1*K4*K5 - 32*K2**2 + 64*K2*K3*K5 - 112*K3**2 - 8*K4**4 + 8*K4**2*K8 - 128*K4**2 - 80*K5**2 - 2*K8**2 + 160 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['5.12'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk5.632', 'vk5.634', 'vk5.772', 'vk5.775', 'vk5.1138', 'vk5.1291', 'vk5.1295', 'vk5.1642', 'vk5.1927', 'vk5.1928'] |
| 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 | O1O2O3O4O5U1U5U4U3U2 |
| R3 orbit | {'O1O2O3O4O5U1U5U4U3U2'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3O4O5U4U3U2U1U5 |
| Gauss code of K* | Same |
| Gauss code of -K* | O1O2O3O4O5U4U3U2U1U5 |
| 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 1 1],[ 4 0 4 3 2 1],[-1 -4 0 0 0 0],[-1 -3 0 0 0 0],[-1 -2 0 0 0 0],[-1 -1 0 0 0 0]] |
| Primitive based matrix | [[ 0 1 1 1 1 -4],[-1 0 0 0 0 -1],[-1 0 0 0 0 -2],[-1 0 0 0 0 -3],[-1 0 0 0 0 -4],[ 4 1 2 3 4 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-1,-1,-1,-1,4,0,0,0,1,0,0,2,0,3,4] |
| Phi over symmetry | [-4,1,1,1,1,1,2,3,4,0,0,0,0,0,0] |
| Phi of -K | [-4,1,1,1,1,1,2,3,4,0,0,0,0,0,0] |
| Phi of K* | [-1,-1,-1,-1,4,0,0,0,1,0,0,2,0,3,4] |
| Phi of -K* | [-4,1,1,1,1,1,2,3,4,0,0,0,0,0,0] |
| Symmetry type of based matrix | + |
| u-polynomial | t^4-4t |
| Normalized Jones-Krushkal polynomial | -z-1 |
| Enhanced Jones-Krushkal polynomial | -8w^4z+8w^3z-w^2z-w |
| Inner characteristic polynomial | t^5+30t^3 |
| Outer characteristic polynomial | t^6+50t^4+20t^2 |
| Flat arrow polynomial | 2*K2**2 - K4 |
| 2-strand cable arrow polynomial | -128*K1**2 + 160*K1*K3*K4 + 96*K1*K4*K5 - 32*K2**2 + 64*K2*K3*K5 - 112*K3**2 - 8*K4**4 + 8*K4**2*K8 - 128*K4**2 - 80*K5**2 - 2*K8**2 + 160 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{1, 5}, {2, 4}, {3}], [{2, 5}, {3, 4}, {1}], [{3, 5}, {4}, {1, 2}]] |
| If K is slice | False |