K12a1099
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q+4-9 q^{-1} +17 q^{-2} -25 q^{-3} +32 q^{-4} -34 q^{-5} +33 q^{-6} -27 q^{-7} +19 q^{-8} -11 q^{-9} +4 q^{-10} - q^{-11} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^4-10 t^3+27 t^2-44 t+51-44 t^{-1} +27 t^{-2} -10 t^{-3} +2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^8+6 z^6+7 z^4+6 z^2+1 }[/math] |
| Determinant | 217 |
| Signature | -4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^6 a^8-3 z^4 a^8-4 z^2 a^8-3 a^8+z^8 a^6+4 z^6 a^6+7 z^4 a^6+8 z^2 a^6+4 a^6+z^8 a^4+4 z^6 a^4+6 z^4 a^4+4 z^2 a^4-z^6 a^2-3 z^4 a^2-2 z^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}-14 z^5 a^{11}+10 z^3 a^{11}-4 z a^{11}+15 z^8 a^{10}-24 z^6 a^{10}+16 z^4 a^{10}-4 z^2 a^{10}+15 z^9 a^9-22 z^7 a^9+9 z^5 a^9+z^3 a^9+10 z^{10} a^8-8 z^8 a^8-4 z^6 a^8-4 z^4 a^8+10 z^2 a^8-3 a^8+3 z^{11} a^7+17 z^9 a^7-55 z^7 a^7+58 z^5 a^7-33 z^3 a^7+8 z a^7+17 z^{10} a^6-42 z^8 a^6+41 z^6 a^6-30 z^4 a^6+15 z^2 a^6-4 a^6+3 z^{11} a^5+9 z^9 a^5-45 z^7 a^5+56 z^5 a^5-32 z^3 a^5+6 z a^5+7 z^{10} a^4-15 z^8 a^4+4 z^6 a^4+5 z^4 a^4-2 z^2 a^4+7 z^9 a^3-21 z^7 a^3+19 z^5 a^3-7 z^3 a^3+2 z a^3+4 z^8 a^2-13 z^6 a^2+12 z^4 a^2-3 z^2 a^2+z^7 a-3 z^5 a+2 z^3 a }[/math] |
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