K12a807
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^3-4 q^2+9 q-17+27 q^{-1} -33 q^{-2} +37 q^{-3} -35 q^{-4} +29 q^{-5} -21 q^{-6} +12 q^{-7} -5 q^{-8} + q^{-9} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -2 t^4+11 t^3-28 t^2+47 t-55+47 t^{-1} -28 t^{-2} +11 t^{-3} -2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -2 z^8-5 z^6-2 z^4+2 z^2+1 }[/math] |
| Determinant | 231 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -a^4 z^8-a^2 z^8+a^6 z^6-3 a^4 z^6-4 a^2 z^6+z^6+2 a^6 z^4-a^4 z^4-6 a^2 z^4+3 z^4+3 a^4 z^2-3 a^2 z^2+2 z^2-a^6+a^4+a^2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 a^5 z^{11}+3 a^3 z^{11}+9 a^6 z^{10}+17 a^4 z^{10}+8 a^2 z^{10}+13 a^7 z^9+16 a^5 z^9+13 a^3 z^9+10 a z^9+11 a^8 z^8-4 a^6 z^8-32 a^4 z^8-9 a^2 z^8+8 z^8+5 a^9 z^7-21 a^7 z^7-40 a^5 z^7-39 a^3 z^7-21 a z^7+4 z^7 a^{-1} +a^{10} z^6-21 a^8 z^6-14 a^6 z^6+25 a^4 z^6-3 a^2 z^6+z^6 a^{-2} -19 z^6-8 a^9 z^5+4 a^7 z^5+27 a^5 z^5+40 a^3 z^5+16 a z^5-9 z^5 a^{-1} -a^{10} z^4+10 a^8 z^4+5 a^6 z^4-10 a^4 z^4+13 a^2 z^4-2 z^4 a^{-2} +15 z^4+3 a^9 z^3+3 a^7 z^3-9 a^5 z^3-16 a^3 z^3-3 a z^3+4 z^3 a^{-1} -a^4 z^2-5 a^2 z^2-4 z^2-a^7 z+a^5 z+3 a^3 z+a z+a^6+a^4-a^2 }[/math] |
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