K12a878
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^4+2 q^3-4 q^2+6 q-8+11 q^{-1} -10 q^{-2} +11 q^{-3} -9 q^{-4} +6 q^{-5} -4 q^{-6} +2 q^{-7} - q^{-8} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^5-3 t^4+6 t^3-9 t^2+12 t-13+12 t^{-1} -9 t^{-2} +6 t^{-3} -3 t^{-4} + t^{-5} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^{10}+7 z^8+17 z^6+17 z^4+7 z^2+1 }[/math] |
| Determinant | 75 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ a^2 z^{10}-a^4 z^8+9 a^2 z^8-z^8-7 a^4 z^6+31 a^2 z^6-7 z^6-17 a^4 z^4+51 a^2 z^4-17 z^4-17 a^4 z^2+41 a^2 z^2-17 z^2-7 a^4+14 a^2-6 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ a^3 z^{11}+a z^{11}+3 a^4 z^{10}+5 a^2 z^{10}+2 z^{10}+3 a^5 z^9-a^3 z^9-2 a z^9+2 z^9 a^{-1} +3 a^6 z^8-16 a^4 z^8-30 a^2 z^8+2 z^8 a^{-2} -9 z^8+3 a^7 z^7-11 a^5 z^7-12 a^3 z^7-6 a z^7-7 z^7 a^{-1} +z^7 a^{-3} +2 a^8 z^6-9 a^6 z^6+38 a^4 z^6+75 a^2 z^6-9 z^6 a^{-2} +17 z^6+a^9 z^5-9 a^7 z^5+15 a^5 z^5+41 a^3 z^5+24 a z^5+3 z^5 a^{-1} -5 z^5 a^{-3} -5 a^8 z^4+9 a^6 z^4-41 a^4 z^4-90 a^2 z^4+10 z^4 a^{-2} -25 z^4-3 a^9 z^3+8 a^7 z^3-3 a^5 z^3-42 a^3 z^3-32 a z^3+3 z^3 a^{-1} +7 z^3 a^{-3} +a^8 z^2-a^6 z^2+26 a^4 z^2+50 a^2 z^2-2 z^2 a^{-2} +20 z^2+a^9 z-3 a^7 z+a^5 z+14 a^3 z+12 a z-3 z a^{-3} -7 a^4-14 a^2-6 }[/math] |
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