K12n287
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^3-4 q^2+8 q-12+17 q^{-1} -18 q^{-2} +18 q^{-3} -15 q^{-4} +10 q^{-5} -6 q^{-6} +2 q^{-7} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^4+6 t^3-15 t^2+22 t-23+22 t^{-1} -15 t^{-2} +6 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^8-2 z^6+z^4+1 }[/math] |
| Determinant | 111 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ a^8-z^4 a^6-4 z^2 a^6-3 a^6+2 z^6 a^4+8 z^4 a^4+9 z^2 a^4+3 a^4-z^8 a^2-5 z^6 a^2-9 z^4 a^2-7 z^2 a^2-a^2+z^6+3 z^4+2 z^2+1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 a^4 z^{10}+2 a^2 z^{10}+5 a^5 z^9+11 a^3 z^9+6 a z^9+4 a^6 z^8+5 a^4 z^8+8 a^2 z^8+7 z^8+a^7 z^7-14 a^5 z^7-32 a^3 z^7-13 a z^7+4 z^7 a^{-1} -8 a^6 z^6-25 a^4 z^6-38 a^2 z^6+z^6 a^{-2} -20 z^6+5 a^7 z^5+30 a^5 z^5+40 a^3 z^5+5 a z^5-10 z^5 a^{-1} +3 a^8 z^4+16 a^6 z^4+42 a^4 z^4+47 a^2 z^4-2 z^4 a^{-2} +16 z^4-10 a^7 z^3-29 a^5 z^3-24 a^3 z^3-a z^3+4 z^3 a^{-1} -4 a^8 z^2-15 a^6 z^2-25 a^4 z^2-20 a^2 z^2-6 z^2+4 a^7 z+10 a^5 z+8 a^3 z+2 a z+a^8+3 a^6+3 a^4+a^2+1 }[/math] |
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