K12a389
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^3-6 q^2+16 q-28+40 q^{-1} -48 q^{-2} +51 q^{-3} -46 q^{-4} +37 q^{-5} -24 q^{-6} +12 q^{-7} -5 q^{-8} + q^{-9} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^4+9 t^3-33 t^2+70 t-89+70 t^{-1} -33 t^{-2} +9 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^8+z^6+z^4+3 z^2+1 }[/math] |
| Determinant | 315 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^2 a^8-3 z^4 a^6-4 z^2 a^6-2 a^6+3 z^6 a^4+7 z^4 a^4+7 z^2 a^4+3 a^4-z^8 a^2-3 z^6 a^2-4 z^4 a^2-z^2 a^2+z^6+z^4 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 5 a^5 z^{11}+5 a^3 z^{11}+13 a^6 z^{10}+30 a^4 z^{10}+17 a^2 z^{10}+15 a^7 z^9+29 a^5 z^9+37 a^3 z^9+23 a z^9+11 a^8 z^8-3 a^6 z^8-38 a^4 z^8-8 a^2 z^8+16 z^8+5 a^9 z^7-19 a^7 z^7-73 a^5 z^7-94 a^3 z^7-39 a z^7+6 z^7 a^{-1} +a^{10} z^6-18 a^8 z^6-31 a^6 z^6-20 a^4 z^6-33 a^2 z^6+z^6 a^{-2} -24 z^6-8 a^9 z^5+41 a^5 z^5+54 a^3 z^5+16 a z^5-5 z^5 a^{-1} -a^{10} z^4+11 a^8 z^4+36 a^6 z^4+40 a^4 z^4+24 a^2 z^4+8 z^4+4 a^9 z^3+11 a^7 z^3+8 a^5 z^3-a z^3-3 a^8 z^2-15 a^6 z^2-16 a^4 z^2-4 a^2 z^2-5 a^7 z-8 a^5 z-4 a^3 z-a z+2 a^6+3 a^4 }[/math] |
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