K12a1163
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^9-2 q^8+5 q^7-9 q^6+12 q^5-15 q^4+16 q^3-15 q^2+12 q-8+5 q^{-1} -2 q^{-2} + q^{-3} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -8 t^2+26 t-35+26 t^{-1} -8 t^{-2} }[/math] |
| Conway polynomial | [math]\displaystyle{ -8 z^4-6 z^2+1 }[/math] |
| Determinant | 103 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -3 z^4 a^{-2} -3 z^4 a^{-4} -z^4 a^{-6} -z^4+a^2 z^2-4 z^2 a^{-2} -4 z^2 a^{-4} +z^2 a^{-8} +a^2- a^{-2} - a^{-4} + a^{-8} +1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{11} a^{-3} +z^{11} a^{-5} +2 z^{10} a^{-2} +4 z^{10} a^{-4} +2 z^{10} a^{-6} +3 z^9 a^{-1} -z^9 a^{-3} -z^9 a^{-5} +3 z^9 a^{-7} -3 z^8 a^{-2} -13 z^8 a^{-4} -4 z^8 a^{-6} +3 z^8 a^{-8} +3 z^8+2 a z^7-8 z^7 a^{-1} +4 z^7 a^{-3} +3 z^7 a^{-5} -9 z^7 a^{-7} +2 z^7 a^{-9} +a^2 z^6-2 z^6 a^{-2} +24 z^6 a^{-4} +6 z^6 a^{-6} -9 z^6 a^{-8} +z^6 a^{-10} -9 z^6-6 a z^5+7 z^5 a^{-1} -12 z^5 a^{-3} -3 z^5 a^{-5} +16 z^5 a^{-7} -6 z^5 a^{-9} -4 a^2 z^4+10 z^4 a^{-2} -20 z^4 a^{-4} -4 z^4 a^{-6} +10 z^4 a^{-8} -4 z^4 a^{-10} +8 z^4+3 a z^3-2 z^3 a^{-1} +19 z^3 a^{-3} +2 z^3 a^{-5} -18 z^3 a^{-7} +4 z^3 a^{-9} +4 a^2 z^2-7 z^2 a^{-2} +11 z^2 a^{-4} -2 z^2 a^{-6} -7 z^2 a^{-8} +4 z^2 a^{-10} -5 z^2-2 z a^{-1} -6 z a^{-3} +4 z a^{-7} -a^2+ a^{-2} - a^{-4} + a^{-8} +1 }[/math] |
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