K12a29
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^3-4 q^2+11 q-19+27 q^{-1} -33 q^{-2} +35 q^{-3} -32 q^{-4} +26 q^{-5} -17 q^{-6} +9 q^{-7} -4 q^{-8} + q^{-9} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^4+7 t^3-24 t^2+48 t-59+48 t^{-1} -24 t^{-2} +7 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^8-z^6-2 z^4-z^2+1 }[/math] |
| Determinant | 219 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^2 a^8+a^8-3 z^4 a^6-7 z^2 a^6-5 a^6+3 z^6 a^4+11 z^4 a^4+17 z^2 a^4+10 a^4-z^8 a^2-5 z^6 a^2-13 z^4 a^2-17 z^2 a^2-9 a^2+z^6+3 z^4+5 z^2+4 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ a^5 z^{11}+a^3 z^{11}+4 a^6 z^{10}+9 a^4 z^{10}+5 a^2 z^{10}+7 a^7 z^9+20 a^5 z^9+23 a^3 z^9+10 a z^9+7 a^8 z^8+16 a^6 z^8+17 a^4 z^8+17 a^2 z^8+9 z^8+4 a^9 z^7-2 a^7 z^7-32 a^5 z^7-43 a^3 z^7-13 a z^7+4 z^7 a^{-1} +a^{10} z^6-13 a^8 z^6-53 a^6 z^6-84 a^4 z^6-65 a^2 z^6+z^6 a^{-2} -19 z^6-9 a^9 z^5-19 a^7 z^5-4 a^5 z^5+12 a^3 z^5-a z^5-7 z^5 a^{-1} -2 a^{10} z^4+9 a^8 z^4+55 a^6 z^4+98 a^4 z^4+74 a^2 z^4-2 z^4 a^{-2} +18 z^4+7 a^9 z^3+22 a^7 z^3+26 a^5 z^3+12 a^3 z^3+5 a z^3+4 z^3 a^{-1} +a^{10} z^2-4 a^8 z^2-26 a^6 z^2-50 a^4 z^2-42 a^2 z^2+z^2 a^{-2} -12 z^2-2 a^9 z-7 a^7 z-9 a^5 z-5 a^3 z-2 a z-z a^{-1} +a^8+5 a^6+10 a^4+9 a^2+4 }[/math] |
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