K12a980
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q+5-12 q^{-1} +22 q^{-2} -31 q^{-3} +39 q^{-4} -41 q^{-5} +38 q^{-6} -31 q^{-7} +21 q^{-8} -11 q^{-9} +4 q^{-10} - q^{-11} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^4-11 t^3+31 t^2-53 t+63-53 t^{-1} +31 t^{-2} -11 t^{-3} +2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^8+5 z^6+5 z^4+4 z^2+1 }[/math] |
| Determinant | 257 |
| Signature | -4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^6 a^8-3 z^4 a^8-4 z^2 a^8-2 a^8+z^8 a^6+4 z^6 a^6+8 z^4 a^6+9 z^2 a^6+3 a^6+z^8 a^4+3 z^6 a^4+2 z^4 a^4-z^2 a^4-a^4-z^6 a^2-2 z^4 a^2+a^2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^5 a^{13}-z^3 a^{13}+4 z^6 a^{12}-3 z^4 a^{12}+10 z^7 a^{11}-12 z^5 a^{11}+8 z^3 a^{11}-2 z a^{11}+17 z^8 a^{10}-28 z^6 a^{10}+24 z^4 a^{10}-7 z^2 a^{10}+19 z^9 a^9-31 z^7 a^9+21 z^5 a^9-5 z^3 a^9+z a^9+13 z^{10} a^8-7 z^8 a^8-21 z^6 a^8+19 z^4 a^8-z^2 a^8-2 a^8+4 z^{11} a^7+25 z^9 a^7-76 z^7 a^7+67 z^5 a^7-30 z^3 a^7+5 z a^7+23 z^{10} a^6-46 z^8 a^6+21 z^6 a^6-10 z^4 a^6+9 z^2 a^6-3 a^6+4 z^{11} a^5+16 z^9 a^5-62 z^7 a^5+54 z^5 a^5-20 z^3 a^5+3 z a^5+10 z^{10} a^4-17 z^8 a^4-3 z^6 a^4+8 z^4 a^4+2 z^2 a^4-a^4+10 z^9 a^3-26 z^7 a^3+19 z^5 a^3-3 z^3 a^3+z a^3+5 z^8 a^2-13 z^6 a^2+10 z^4 a^2-z^2 a^2-a^2+z^7 a-2 z^5 a+z^3 a }[/math] |
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