K12a1220
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -1+3 q^{-1} -4 q^{-2} +8 q^{-3} -10 q^{-4} +12 q^{-5} -13 q^{-6} +12 q^{-7} -11 q^{-8} +8 q^{-9} -5 q^{-10} +3 q^{-11} - q^{-12} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^5-4 t^4+8 t^3-11 t^2+14 t-15+14 t^{-1} -11 t^{-2} +8 t^{-3} -4 t^{-4} + t^{-5} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^{10}+6 z^8+11 z^6+7 z^4+3 z^2+1 }[/math] |
| Determinant | 91 |
| Signature | -6 |
| HOMFLY-PT polynomial | [math]\displaystyle{ a^6 z^{10}-a^8 z^8+8 a^6 z^8-a^4 z^8-6 a^8 z^6+23 a^6 z^6-6 a^4 z^6-11 a^8 z^4+28 a^6 z^4-10 a^4 z^4-6 a^8 z^2+11 a^6 z^2-2 a^4 z^2-2 a^6+3 a^4 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^3 a^{15}+3 z^4 a^{14}-z^2 a^{14}+5 z^5 a^{13}-3 z^3 a^{13}+7 z^6 a^{12}-8 z^4 a^{12}+9 z^7 a^{11}-19 z^5 a^{11}+9 z^3 a^{11}-2 z a^{11}+9 z^8 a^{10}-24 z^6 a^{10}+13 z^4 a^{10}-z^2 a^{10}+7 z^9 a^9-19 z^7 a^9+2 z^5 a^9+13 z^3 a^9-4 z a^9+5 z^{10} a^8-17 z^8 a^8+12 z^6 a^8-4 z^4 a^8+6 z^2 a^8+2 z^{11} a^7-3 z^9 a^7-16 z^7 a^7+30 z^5 a^7-8 z^3 a^7-4 z a^7+8 z^{10} a^6-46 z^8 a^6+88 z^6 a^6-66 z^4 a^6+15 z^2 a^6+2 a^6+2 z^{11} a^5-9 z^9 a^5+6 z^7 a^5+15 z^5 a^5-14 z^3 a^5-z a^5+3 z^{10} a^4-20 z^8 a^4+45 z^6 a^4-38 z^4 a^4+7 z^2 a^4+3 a^4+z^9 a^3-6 z^7 a^3+11 z^5 a^3-6 z^3 a^3+z a^3 }[/math] |
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