K12a641
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^3+2 q^2-4 q+7-8 q^{-1} +10 q^{-2} -10 q^{-3} +10 q^{-4} -8 q^{-5} +6 q^{-6} -4 q^{-7} +2 q^{-8} - q^{-9} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^4-6 t^3+10 t^2-12 t+13-12 t^{-1} +10 t^{-2} -6 t^{-3} +2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^8+10 z^6+14 z^4+6 z^2+1 }[/math] |
| Determinant | 73 |
| 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+12 a^2 z^4-5 z^4-7 a^6 z^2+10 a^4 z^2+10 a^2 z^2-7 z^2-3 a^6+3 a^4+3 a^2-2 }[/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^8-5 z^4 a^8+2 z^2 a^8+5 z^7 a^7-10 z^5 a^7+4 z^3 a^7-z a^7+6 z^8 a^6-19 z^6 a^6+19 z^4 a^6-13 z^2 a^6+3 a^6+5 z^9 a^5-16 z^7 a^5+9 z^5 a^5+2 z^3 a^5-3 z a^5+3 z^{10} a^4-7 z^8 a^4-11 z^6 a^4+28 z^4 a^4-16 z^2 a^4+3 a^4+z^{11} a^3+2 z^9 a^3-26 z^7 a^3+42 z^5 a^3-20 z^3 a^3+4 z a^3+5 z^{10} a^2-26 z^8 a^2+41 z^6 a^2-25 z^4 a^2+11 z^2 a^2-3 a^2+z^{11} a-2 z^9 a-12 z^7 a+37 z^5 a-31 z^3 a+8 z a+2 z^{10}-13 z^8+29 z^6-27 z^4+11 z^2-2+z^9 a^{-1} -7 z^7 a^{-1} +17 z^5 a^{-1} -16 z^3 a^{-1} +4 z a^{-1} }[/math] |
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