K12a759
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^3+2 q^2-3 q+5-6 q^{-1} +8 q^{-2} -8 q^{-3} +8 q^{-4} -7 q^{-5} +6 q^{-6} -4 q^{-7} +2 q^{-8} - q^{-9} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^4-6 t^3+9 t^2-9 t+9-9 t^{-1} +9 t^{-2} -6 t^{-3} +2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^8+10 z^6+13 z^4+5 z^2+1 }[/math] |
| Determinant | 61 |
| Signature | -4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ a^4 z^8+a^2 z^8-a^6 z^6+6 a^4 z^6+6 a^2 z^6-z^6-5 a^6 z^4+12 a^4 z^4+11 a^2 z^4-5 z^4-7 a^6 z^2+11 a^4 z^2+7 a^2 z^2-6 z^2-3 a^6+4 a^4+a^2-1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^3 a^{11}-z a^{11}+2 z^4 a^{10}-z^2 a^{10}+3 z^5 a^9-2 z^3 a^9+z a^9+4 z^6 a^8-6 z^4 a^8+4 z^2 a^8+4 z^7 a^7-7 z^5 a^7+2 z^3 a^7+4 z^8 a^6-11 z^6 a^6+10 z^4 a^6-9 z^2 a^6+3 a^6+3 z^9 a^5-8 z^7 a^5+z^5 a^5+4 z^3 a^5-3 z a^5+2 z^{10} a^4-5 z^8 a^4-6 z^6 a^4+19 z^4 a^4-15 z^2 a^4+4 a^4+z^{11} a^3-2 z^9 a^3-6 z^7 a^3+11 z^5 a^3-2 z^3 a^3+4 z^{10} a^2-23 z^8 a^2+42 z^6 a^2-30 z^4 a^2+10 z^2 a^2-a^2+z^{11} a-4 z^9 a-z^7 a+16 z^5 a-14 z^3 a+3 z a+2 z^{10}-14 z^8+33 z^6-31 z^4+11 z^2-1+z^9 a^{-1} -7 z^7 a^{-1} +16 z^5 a^{-1} -13 z^3 a^{-1} +2 z a^{-1} }[/math] |
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