K13a3170
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Polynomial invariants
| Jones polynomial | Data:K13a3170/Jones Polynomial |
| Alexander polynomial | [math]\displaystyle{ t^5-6 t^4+19 t^3-40 t^2+63 t-73+63 t^{-1} -40 t^{-2} +19 t^{-3} -6 t^{-4} + t^{-5} }[/math] |
| Conway polynomial | Data:K13a3170/Conway Polynomial |
| Determinant | 331 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^{10} a^{-2} +7 z^8 a^{-2} -2 z^8 a^{-4} -z^8+21 z^6 a^{-2} -11 z^6 a^{-4} +z^6 a^{-6} -5 z^6+33 z^4 a^{-2} -23 z^4 a^{-4} +4 z^4 a^{-6} -10 z^4+27 z^2 a^{-2} -20 z^2 a^{-4} +5 z^2 a^{-6} -9 z^2+9 a^{-2} -6 a^{-4} + a^{-6} -3 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{12} a^{-2} +2 z^{12} a^{-4} +8 z^{11} a^{-1} +16 z^{11} a^{-3} +8 z^{11} a^{-5} +27 z^{10} a^{-2} +28 z^{10} a^{-4} +13 z^{10} a^{-6} +12 z^{10}+9 a z^9-z^9 a^{-1} -16 z^9 a^{-3} +6 z^9 a^{-5} +12 z^9 a^{-7} +4 a^2 z^8-97 z^8 a^{-2} -90 z^8 a^{-4} -21 z^8 a^{-6} +8 z^8 a^{-8} -32 z^8+a^3 z^7-26 a z^7-48 z^7 a^{-1} -46 z^7 a^{-3} -49 z^7 a^{-5} -20 z^7 a^{-7} +4 z^7 a^{-9} -11 a^2 z^6+132 z^6 a^{-2} +119 z^6 a^{-4} +17 z^6 a^{-6} -13 z^6 a^{-8} +z^6 a^{-10} +33 z^6-3 a^3 z^5+27 a z^5+81 z^5 a^{-1} +103 z^5 a^{-3} +72 z^5 a^{-5} +12 z^5 a^{-7} -8 z^5 a^{-9} +8 a^2 z^4-97 z^4 a^{-2} -83 z^4 a^{-4} -12 z^4 a^{-6} +5 z^4 a^{-8} -2 z^4 a^{-10} -25 z^4+2 a^3 z^3-17 a z^3-58 z^3 a^{-1} -74 z^3 a^{-3} -43 z^3 a^{-5} -3 z^3 a^{-7} +5 z^3 a^{-9} -2 a^2 z^2+41 z^2 a^{-2} +34 z^2 a^{-4} +6 z^2 a^{-6} +z^2 a^{-10} +12 z^2+5 a z+15 z a^{-1} +19 z a^{-3} +9 z a^{-5} -z a^{-7} -z a^{-9} -9 a^{-2} -6 a^{-4} - a^{-6} -3 }[/math] |
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