K12a78
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q+3-7 q^{-1} +13 q^{-2} -17 q^{-3} +22 q^{-4} -23 q^{-5} +22 q^{-6} -18 q^{-7} +12 q^{-8} -7 q^{-9} +3 q^{-10} - q^{-11} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^4-8 t^3+19 t^2-29 t+33-29 t^{-1} +19 t^{-2} -8 t^{-3} +2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^8+8 z^6+11 z^4+7 z^2+1 }[/math] |
| Determinant | 149 |
| 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+6 z^2 a^6+z^8 a^4+5 z^6 a^4+10 z^4 a^4+11 z^2 a^4+5 a^4-z^6 a^2-4 z^4 a^2-5 z^2 a^2-2 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}-7 z^6 a^{10}+3 z^4 a^{10}-z^2 a^{10}+6 z^9 a^9-8 z^7 a^9+7 z^5 a^9-4 z^3 a^9+2 z a^9+4 z^{10} a^8-2 z^8 a^8-2 z^6 a^8+5 z^2 a^8-2 a^8+z^{11} a^7+10 z^9 a^7-30 z^7 a^7+33 z^5 a^7-17 z^3 a^7+4 z a^7+7 z^{10} a^6-12 z^8 a^6+5 z^4 a^6-z^2 a^6+z^{11} a^5+8 z^9 a^5-28 z^7 a^5+23 z^5 a^5-5 z^3 a^5-2 z a^5+3 z^{10} a^4-z^8 a^4-19 z^6 a^4+26 z^4 a^4-16 z^2 a^4+5 a^4+4 z^9 a^3-10 z^7 a^3+z^5 a^3+8 z^3 a^3-4 z a^3+3 z^8 a^2-11 z^6 a^2+13 z^4 a^2-7 z^2 a^2+2 a^2+z^7 a-4 z^5 a+5 z^3 a-2 z a }[/math] |
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