K12a512
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^4+4 q^3-8 q^2+13 q-18+22 q^{-1} -23 q^{-2} +22 q^{-3} -17 q^{-4} +12 q^{-5} -7 q^{-6} +3 q^{-7} - q^{-8} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^4+7 t^3-19 t^2+31 t-35+31 t^{-1} -19 t^{-2} +7 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^8-z^6+3 z^4+2 z^2+1 }[/math] |
| Determinant | 151 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -a^2 z^8+2 a^4 z^6-5 a^2 z^6+2 z^6-a^6 z^4+8 a^4 z^4-10 a^2 z^4-z^4 a^{-2} +7 z^4-3 a^6 z^2+10 a^4 z^2-9 a^2 z^2-2 z^2 a^{-2} +6 z^2-2 a^6+4 a^4-2 a^2+1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ a^3 z^{11}+a z^{11}+3 a^4 z^{10}+7 a^2 z^{10}+4 z^{10}+5 a^5 z^9+9 a^3 z^9+10 a z^9+6 z^9 a^{-1} +6 a^6 z^8+5 a^4 z^8-10 a^2 z^8+4 z^8 a^{-2} -5 z^8+5 a^7 z^7-2 a^5 z^7-23 a^3 z^7-37 a z^7-20 z^7 a^{-1} +z^7 a^{-3} +3 a^8 z^6-8 a^6 z^6-21 a^4 z^6-10 a^2 z^6-14 z^6 a^{-2} -14 z^6+a^9 z^5-7 a^7 z^5-6 a^5 z^5+16 a^3 z^5+35 a z^5+18 z^5 a^{-1} -3 z^5 a^{-3} -5 a^8 z^4+7 a^6 z^4+26 a^4 z^4+21 a^2 z^4+13 z^4 a^{-2} +20 z^4-2 a^9 z^3+3 a^7 z^3+8 a^5 z^3-a^3 z^3-11 a z^3-5 z^3 a^{-1} +2 z^3 a^{-3} +2 a^8 z^2-6 a^6 z^2-15 a^4 z^2-11 a^2 z^2-3 z^2 a^{-2} -7 z^2+a^9 z-a^7 z-3 a^5 z-a^3 z+2 a^6+4 a^4+2 a^2+1 }[/math] |
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