K12a193
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^2-2 q+5-8 q^{-1} +11 q^{-2} -14 q^{-3} +16 q^{-4} -15 q^{-5} +13 q^{-6} -10 q^{-7} +6 q^{-8} -3 q^{-9} + q^{-10} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-7 t^3+16 t^2-19 t+19-19 t^{-1} +16 t^{-2} -7 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8+z^6-6 z^4-2 z^2+1 }[/math] |
| Determinant | 105 |
| Signature | -4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^4 a^8+3 z^2 a^8+a^8-2 z^6 a^6-8 z^4 a^6-8 z^2 a^6-3 a^6+z^8 a^4+5 z^6 a^4+9 z^4 a^4+10 z^2 a^4+5 a^4-2 z^6 a^2-9 z^4 a^2-11 z^2 a^2-5 a^2+z^4+4 z^2+3 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^4 a^{12}-z^2 a^{12}+3 z^5 a^{11}-3 z^3 a^{11}+z a^{11}+5 z^6 a^{10}-5 z^4 a^{10}+2 z^2 a^{10}+6 z^7 a^9-6 z^5 a^9+z^3 a^9+z a^9+6 z^8 a^8-8 z^6 a^8+4 z^4 a^8-3 z^2 a^8+a^8+5 z^9 a^7-8 z^7 a^7+3 z^5 a^7-2 z^3 a^7+3 z^{10} a^6-2 z^8 a^6-13 z^6 a^6+20 z^4 a^6-14 z^2 a^6+3 a^6+z^{11} a^5+4 z^9 a^5-21 z^7 a^5+20 z^5 a^5-5 z^3 a^5+5 z^{10} a^4-15 z^8 a^4+z^6 a^4+23 z^4 a^4-19 z^2 a^4+5 a^4+z^{11} a^3+z^9 a^3-17 z^7 a^3+23 z^5 a^3-7 z^3 a^3+z a^3+2 z^{10} a^2-6 z^8 a^2-5 z^6 a^2+25 z^4 a^2-21 z^2 a^2+5 a^2+2 z^9 a-10 z^7 a+15 z^5 a-8 z^3 a+z a+z^8-6 z^6+12 z^4-10 z^2+3 }[/math] |
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