K12a19
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^3-4 q^2+9 q-15+23 q^{-1} -28 q^{-2} +30 q^{-3} -28 q^{-4} +23 q^{-5} -16 q^{-6} +9 q^{-7} -4 q^{-8} + q^{-9} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^4+7 t^3-22 t^2+41 t-49+41 t^{-1} -22 t^{-2} +7 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^8-z^6+1 }[/math] |
| Determinant | 191 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^2 a^8+a^8-3 z^4 a^6-7 z^2 a^6-4 a^6+3 z^6 a^4+11 z^4 a^4+14 z^2 a^4+6 a^4-z^8 a^2-5 z^6 a^2-11 z^4 a^2-11 z^2 a^2-4 a^2+z^6+3 z^4+3 z^2+2 }[/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+17 a^5 z^9+19 a^3 z^9+9 a z^9+7 a^8 z^8+9 a^6 z^8-2 a^4 z^8+4 a^2 z^8+8 z^8+4 a^9 z^7-7 a^7 z^7-43 a^5 z^7-57 a^3 z^7-21 a z^7+4 z^7 a^{-1} +a^{10} z^6-14 a^8 z^6-37 a^6 z^6-38 a^4 z^6-38 a^2 z^6+z^6 a^{-2} -21 z^6-9 a^9 z^5-7 a^7 z^5+41 a^5 z^5+66 a^3 z^5+18 a z^5-9 z^5 a^{-1} -2 a^{10} z^4+8 a^8 z^4+38 a^6 z^4+63 a^4 z^4+55 a^2 z^4-2 z^4 a^{-2} +18 z^4+6 a^9 z^3+6 a^7 z^3-19 a^5 z^3-30 a^3 z^3-8 a z^3+3 z^3 a^{-1} +a^{10} z^2-3 a^8 z^2-20 a^6 z^2-35 a^4 z^2-27 a^2 z^2-8 z^2-a^9 z-a^7 z+3 a^5 z+5 a^3 z+2 a z+a^8+4 a^6+6 a^4+4 a^2+2 }[/math] |
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