K12a223
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^4-4 q^3+9 q^2-16 q+23-27 q^{-1} +30 q^{-2} -27 q^{-3} +22 q^{-4} -16 q^{-5} +9 q^{-6} -4 q^{-7} + q^{-8} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -3 t^3+18 t^2-44 t+59-44 t^{-1} +18 t^{-2} -3 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -3 z^6+z^2+1 }[/math] |
| Determinant | 189 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ a^8-4 z^2 a^6-4 a^6+5 z^4 a^4+10 z^2 a^4+5 a^4-2 z^6 a^2-5 z^4 a^2-6 z^2 a^2-2 a^2-z^6-z^4+1+z^4 a^{-2} +z^2 a^{-2} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 a^5 z^{11}+2 a^3 z^{11}+5 a^6 z^{10}+14 a^4 z^{10}+9 a^2 z^{10}+4 a^7 z^9+11 a^5 z^9+24 a^3 z^9+17 a z^9+a^8 z^8-14 a^6 z^8-33 a^4 z^8+a^2 z^8+19 z^8-17 a^7 z^7-67 a^5 z^7-97 a^3 z^7-32 a z^7+15 z^7 a^{-1} -4 a^8 z^6-a^6 z^6-14 a^4 z^6-61 a^2 z^6+9 z^6 a^{-2} -35 z^6+25 a^7 z^5+96 a^5 z^5+106 a^3 z^5+12 a z^5-19 z^5 a^{-1} +4 z^5 a^{-3} +6 a^8 z^4+27 a^6 z^4+65 a^4 z^4+73 a^2 z^4-6 z^4 a^{-2} +z^4 a^{-4} +22 z^4-15 a^7 z^3-50 a^5 z^3-47 a^3 z^3-4 a z^3+7 z^3 a^{-1} -z^3 a^{-3} -4 a^8 z^2-20 a^6 z^2-37 a^4 z^2-30 a^2 z^2+z^2 a^{-2} -8 z^2+3 a^7 z+10 a^5 z+10 a^3 z+3 a z+a^8+4 a^6+5 a^4+2 a^2+1 }[/math] |
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