K12a190
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q+5-10 q^{-1} +18 q^{-2} -26 q^{-3} +32 q^{-4} -34 q^{-5} +32 q^{-6} -26 q^{-7} +18 q^{-8} -10 q^{-9} +4 q^{-10} - q^{-11} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-8 t^3+26 t^2-46 t+55-46 t^{-1} +26 t^{-2} -8 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8-2 z^4+2 z^2+1 }[/math] |
| Determinant | 217 |
| Signature | -4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^2 a^{10}-a^{10}+3 z^4 a^8+6 z^2 a^8+2 a^8-3 z^6 a^6-9 z^4 a^6-7 z^2 a^6-a^6+z^8 a^4+4 z^6 a^4+6 z^4 a^4+3 z^2 a^4-a^4-z^6 a^2-2 z^4 a^2+z^2 a^2+2 a^2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^5 a^{13}-z^3 a^{13}+4 z^6 a^{12}-4 z^4 a^{12}+z^2 a^{12}+9 z^7 a^{11}-12 z^5 a^{11}+8 z^3 a^{11}-2 z a^{11}+13 z^8 a^{10}-19 z^6 a^{10}+14 z^4 a^{10}-5 z^2 a^{10}+a^{10}+12 z^9 a^9-10 z^7 a^9-6 z^5 a^9+8 z^3 a^9-z a^9+7 z^{10} a^8+9 z^8 a^8-40 z^6 a^8+35 z^4 a^8-14 z^2 a^8+2 a^8+2 z^{11} a^7+21 z^9 a^7-54 z^7 a^7+42 z^5 a^7-18 z^3 a^7+3 z a^7+14 z^{10} a^6-18 z^8 a^6-19 z^6 a^6+31 z^4 a^6-13 z^2 a^6+a^6+2 z^{11} a^5+18 z^9 a^5-64 z^7 a^5+63 z^5 a^5-24 z^3 a^5+3 z a^5+7 z^{10} a^4-9 z^8 a^4-17 z^6 a^4+25 z^4 a^4-4 z^2 a^4-a^4+9 z^9 a^3-28 z^7 a^3+26 z^5 a^3-7 z^3 a^3+z a^3+5 z^8 a^2-15 z^6 a^2+11 z^4 a^2+z^2 a^2-2 a^2+z^7 a-2 z^5 a }[/math] |
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