K12a1219
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^4+3 q^3-6 q^2+10 q-14+18 q^{-1} -18 q^{-2} +18 q^{-3} -15 q^{-4} +10 q^{-5} -6 q^{-6} +3 q^{-7} - q^{-8} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^5-4 t^4+9 t^3-15 t^2+21 t-23+21 t^{-1} -15 t^{-2} +9 t^{-3} -4 t^{-4} + t^{-5} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^{10}+6 z^8+12 z^6+9 z^4+3 z^2+1 }[/math] |
| Determinant | 123 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ a^2 z^{10}-a^4 z^8+8 a^2 z^8-z^8-6 a^4 z^6+24 a^2 z^6-6 z^6-12 a^4 z^4+33 a^2 z^4-12 z^4-9 a^4 z^2+21 a^2 z^2-9 z^2-3 a^4+6 a^2-2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 a^3 z^{11}+2 a z^{11}+5 a^4 z^{10}+9 a^2 z^{10}+4 z^{10}+6 a^5 z^9-a^3 z^9-3 a z^9+4 z^9 a^{-1} +6 a^6 z^8-17 a^4 z^8-41 a^2 z^8+3 z^8 a^{-2} -15 z^8+5 a^7 z^7-16 a^5 z^7-12 a^3 z^7-6 a z^7-14 z^7 a^{-1} +z^7 a^{-3} +3 a^8 z^6-14 a^6 z^6+30 a^4 z^6+81 a^2 z^6-12 z^6 a^{-2} +22 z^6+a^9 z^5-11 a^7 z^5+17 a^5 z^5+30 a^3 z^5+16 a z^5+11 z^5 a^{-1} -4 z^5 a^{-3} -6 a^8 z^4+12 a^6 z^4-24 a^4 z^4-78 a^2 z^4+12 z^4 a^{-2} -24 z^4-2 a^9 z^3+7 a^7 z^3-a^5 z^3-22 a^3 z^3-17 a z^3-z^3 a^{-1} +4 z^3 a^{-3} +a^8 z^2-2 a^6 z^2+13 a^4 z^2+31 a^2 z^2-2 z^2 a^{-2} +13 z^2-2 a^7 z+5 a^3 z+4 a z-z a^{-3} -3 a^4-6 a^2-2 }[/math] |
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