K12a174
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^4+4 q^3-9 q^2+15 q-20+25 q^{-1} -26 q^{-2} +24 q^{-3} -19 q^{-4} +13 q^{-5} -7 q^{-6} +3 q^{-7} - q^{-8} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^4+7 t^3-20 t^2+35 t-41+35 t^{-1} -20 t^{-2} +7 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^8-z^6+2 z^4+2 z^2+1 }[/math] |
| Determinant | 167 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -a^2 z^8+2 a^4 z^6-5 a^2 z^6+2 z^6-a^6 z^4+8 a^4 z^4-11 a^2 z^4-z^4 a^{-2} +7 z^4-3 a^6 z^2+11 a^4 z^2-12 a^2 z^2-2 z^2 a^{-2} +8 z^2-2 a^6+5 a^4-5 a^2- a^{-2} +4 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ a^3 z^{11}+a z^{11}+4 a^4 z^{10}+8 a^2 z^{10}+4 z^{10}+7 a^5 z^9+15 a^3 z^9+14 a z^9+6 z^9 a^{-1} +7 a^6 z^8+6 a^4 z^8-4 a^2 z^8+4 z^8 a^{-2} +z^8+5 a^7 z^7-10 a^5 z^7-45 a^3 z^7-47 a z^7-16 z^7 a^{-1} +z^7 a^{-3} +3 a^8 z^6-11 a^6 z^6-35 a^4 z^6-43 a^2 z^6-13 z^6 a^{-2} -35 z^6+a^9 z^5-6 a^7 z^5+8 a^5 z^5+43 a^3 z^5+38 a z^5+7 z^5 a^{-1} -3 z^5 a^{-3} -5 a^8 z^4+11 a^6 z^4+51 a^4 z^4+67 a^2 z^4+13 z^4 a^{-2} +45 z^4-2 a^9 z^3+a^7 z^3-2 a^5 z^3-12 a^3 z^3-7 a z^3+3 z^3 a^{-1} +3 z^3 a^{-3} +2 a^8 z^2-8 a^6 z^2-28 a^4 z^2-33 a^2 z^2-6 z^2 a^{-2} -21 z^2+a^9 z-a^5 z-a z-2 z a^{-1} -z a^{-3} +2 a^6+5 a^4+5 a^2+ a^{-2} +4 }[/math] |
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