K12a573
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^5-4 q^4+8 q^3-13 q^2+18 q-20+22 q^{-1} -20 q^{-2} +16 q^{-3} -11 q^{-4} +6 q^{-5} -3 q^{-6} + q^{-7} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -2 t^4+9 t^3-19 t^2+27 t-29+27 t^{-1} -19 t^{-2} +9 t^{-3} -2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -2 z^8-7 z^6-5 z^4+1 }[/math] |
| Determinant | 143 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -a^2 z^8-z^8+a^4 z^6-5 a^2 z^6+z^6 a^{-2} -4 z^6+4 a^4 z^4-9 a^2 z^4+3 z^4 a^{-2} -3 z^4+4 a^4 z^2-8 a^2 z^2+z^2 a^{-2} +3 z^2+a^4-3 a^2- a^{-2} +4 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 a z^{11}+2 z^{11} a^{-1} +6 a^2 z^{10}+5 z^{10} a^{-2} +11 z^{10}+9 a^3 z^9+9 a z^9+4 z^9 a^{-1} +4 z^9 a^{-3} +9 a^4 z^8-7 a^2 z^8-19 z^8 a^{-2} +z^8 a^{-4} -36 z^8+7 a^5 z^7-19 a^3 z^7-49 a z^7-41 z^7 a^{-1} -18 z^7 a^{-3} +5 a^6 z^6-16 a^4 z^6-20 a^2 z^6+17 z^6 a^{-2} -4 z^6 a^{-4} +22 z^6+3 a^7 z^5-7 a^5 z^5+10 a^3 z^5+52 a z^5+57 z^5 a^{-1} +25 z^5 a^{-3} +a^8 z^4-4 a^6 z^4+11 a^4 z^4+31 a^2 z^4+z^4 a^{-2} +5 z^4 a^{-4} +11 z^4-3 a^7 z^3+a^5 z^3-a^3 z^3-15 a z^3-21 z^3 a^{-1} -11 z^3 a^{-3} -a^8 z^2+a^6 z^2-5 a^4 z^2-16 a^2 z^2-4 z^2 a^{-2} -2 z^2 a^{-4} -11 z^2+a^7 z+a^5 z-a^3 z-a z+a^4+3 a^2+ a^{-2} +4 }[/math] |
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