K12a219
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q+4-8 q^{-1} +15 q^{-2} -21 q^{-3} +26 q^{-4} -28 q^{-5} +27 q^{-6} -22 q^{-7} +15 q^{-8} -9 q^{-9} +4 q^{-10} - q^{-11} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-7 t^3+22 t^2-38 t+45-38 t^{-1} +22 t^{-2} -7 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8+z^6+3 z^2+1 }[/math] |
| Determinant | 181 |
| Signature | -4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^2 a^{10}-a^{10}+3 z^4 a^8+7 z^2 a^8+3 a^8-3 z^6 a^6-11 z^4 a^6-13 z^2 a^6-5 a^6+z^8 a^4+5 z^6 a^4+11 z^4 a^4+12 z^2 a^4+4 a^4-z^6 a^2-3 z^4 a^2-2 z^2 a^2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^5 a^{13}-z^3 a^{13}+4 z^6 a^{12}-5 z^4 a^{12}+z^2 a^{12}+8 z^7 a^{11}-12 z^5 a^{11}+7 z^3 a^{11}-2 z a^{11}+10 z^8 a^{10}-14 z^6 a^{10}+9 z^4 a^{10}-4 z^2 a^{10}+a^{10}+8 z^9 a^9-2 z^7 a^9-15 z^5 a^9+14 z^3 a^9-2 z a^9+4 z^{10} a^8+13 z^8 a^8-44 z^6 a^8+43 z^4 a^8-17 z^2 a^8+3 a^8+z^{11} a^7+16 z^9 a^7-36 z^7 a^7+21 z^5 a^7-3 z^3 a^7+8 z^{10} a^6-z^8 a^6-42 z^6 a^6+57 z^4 a^6-29 z^2 a^6+5 a^6+z^{11} a^5+14 z^9 a^5-45 z^7 a^5+41 z^5 a^5-15 z^3 a^5+z a^5+4 z^{10} a^4-30 z^6 a^4+43 z^4 a^4-22 z^2 a^4+4 a^4+6 z^9 a^3-18 z^7 a^3+15 z^5 a^3-4 z^3 a^3+z a^3+4 z^8 a^2-14 z^6 a^2+15 z^4 a^2-5 z^2 a^2+z^7 a-3 z^5 a+2 z^3 a }[/math] |
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