K12a533
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q+3-6 q^{-1} +11 q^{-2} -15 q^{-3} +20 q^{-4} -21 q^{-5} +20 q^{-6} -17 q^{-7} +12 q^{-8} -7 q^{-9} +3 q^{-10} - q^{-11} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^4-8 t^3+18 t^2-26 t+29-26 t^{-1} +18 t^{-2} -8 t^{-3} +2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^8+8 z^6+10 z^4+6 z^2+1 }[/math] |
| Determinant | 137 |
| Signature | -4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^6 a^8-4 z^4 a^8-5 z^2 a^8-2 a^8+z^8 a^6+5 z^6 a^6+9 z^4 a^6+7 z^2 a^6+a^6+z^8 a^4+5 z^6 a^4+9 z^4 a^4+8 z^2 a^4+3 a^4-z^6 a^2-4 z^4 a^2-4 z^2 a^2-a^2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^5 a^{13}-2 z^3 a^{13}+z a^{13}+3 z^6 a^{12}-5 z^4 a^{12}+2 z^2 a^{12}+5 z^7 a^{11}-7 z^5 a^{11}+3 z^3 a^{11}-z a^{11}+6 z^8 a^{10}-8 z^6 a^{10}+5 z^4 a^{10}-2 z^2 a^{10}+5 z^9 a^9-4 z^7 a^9+z^3 a^9+3 z^{10} a^8+z^8 a^8-5 z^6 a^8+5 z^2 a^8-2 a^8+z^{11} a^7+6 z^9 a^7-15 z^7 a^7+13 z^5 a^7-6 z^3 a^7+z a^7+6 z^{10} a^6-13 z^8 a^6+11 z^6 a^6-9 z^4 a^6+5 z^2 a^6-a^6+z^{11} a^5+5 z^9 a^5-20 z^7 a^5+18 z^5 a^5-4 z^3 a^5-2 z a^5+3 z^{10} a^4-5 z^8 a^4-7 z^6 a^4+15 z^4 a^4-10 z^2 a^4+3 a^4+4 z^9 a^3-13 z^7 a^3+9 z^5 a^3+2 z^3 a^3-2 z a^3+3 z^8 a^2-12 z^6 a^2+14 z^4 a^2-6 z^2 a^2+a^2+z^7 a-4 z^5 a+4 z^3 a-z a }[/math] |
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