K12a176
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^5-3 q^4+6 q^3-10 q^2+15 q-18+20 q^{-1} -19 q^{-2} +16 q^{-3} -12 q^{-4} +7 q^{-5} -3 q^{-6} + q^{-7} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^3-13 t^2+31 t-39+31 t^{-1} -13 t^{-2} +2 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^6-z^4-3 z^2+1 }[/math] |
| Determinant | 131 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^2 a^6+a^6-2 z^4 a^4-3 z^2 a^4-a^4+z^6 a^2+z^4 a^2-z^2 a^2-a^2+z^6+2 z^4+3 z^2+3-2 z^4 a^{-2} -4 z^2 a^{-2} -2 a^{-2} +z^2 a^{-4} + a^{-4} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ a z^{11}+z^{11} a^{-1} +4 a^2 z^{10}+3 z^{10} a^{-2} +7 z^{10}+7 a^3 z^9+10 a z^9+6 z^9 a^{-1} +3 z^9 a^{-3} +9 a^4 z^8-10 z^8 a^{-2} +z^8 a^{-4} -20 z^8+9 a^5 z^7-7 a^3 z^7-41 a z^7-40 z^7 a^{-1} -15 z^7 a^{-3} +6 a^6 z^6-12 a^4 z^6-18 a^2 z^6+2 z^6 a^{-2} -5 z^6 a^{-4} +7 z^6+3 a^7 z^5-14 a^5 z^5-9 a^3 z^5+47 a z^5+63 z^5 a^{-1} +24 z^5 a^{-3} +a^8 z^4-6 a^6 z^4+a^4 z^4+13 a^2 z^4+16 z^4 a^{-2} +8 z^4 a^{-4} +13 z^4-2 a^7 z^3+12 a^5 z^3+9 a^3 z^3-27 a z^3-36 z^3 a^{-1} -14 z^3 a^{-3} -a^8 z^2+4 a^6 z^2+5 a^4 z^2-5 a^2 z^2-11 z^2 a^{-2} -5 z^2 a^{-4} -11 z^2-3 a^5 z-2 a^3 z+5 a z+7 z a^{-1} +3 z a^{-3} -a^6-a^4+a^2+2 a^{-2} + a^{-4} +3 }[/math] |
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