K12a285
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^4+5 q^3-11 q^2+20 q-28+34 q^{-1} -36 q^{-2} +33 q^{-3} -27 q^{-4} +18 q^{-5} -9 q^{-6} +4 q^{-7} - q^{-8} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^4+8 t^3-27 t^2+49 t-57+49 t^{-1} -27 t^{-2} +8 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^8+z^4-3 z^2+1 }[/math] |
| Determinant | 227 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -a^2 z^8+2 a^4 z^6-4 a^2 z^6+2 z^6-a^6 z^4+6 a^4 z^4-8 a^2 z^4-z^4 a^{-2} +5 z^4-2 a^6 z^2+6 a^4 z^2-9 a^2 z^2-z^2 a^{-2} +3 z^2+2 a^4-3 a^2+ a^{-2} +1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 a^3 z^{11}+2 a z^{11}+8 a^4 z^{10}+15 a^2 z^{10}+7 z^{10}+13 a^5 z^9+26 a^3 z^9+22 a z^9+9 z^9 a^{-1} +12 a^6 z^8+7 a^4 z^8-13 a^2 z^8+5 z^8 a^{-2} -3 z^8+8 a^7 z^7-16 a^5 z^7-71 a^3 z^7-72 a z^7-24 z^7 a^{-1} +z^7 a^{-3} +4 a^8 z^6-15 a^6 z^6-43 a^4 z^6-44 a^2 z^6-14 z^6 a^{-2} -34 z^6+a^9 z^5-9 a^7 z^5+5 a^5 z^5+58 a^3 z^5+63 a z^5+18 z^5 a^{-1} -2 z^5 a^{-3} -5 a^8 z^4+7 a^6 z^4+44 a^4 z^4+61 a^2 z^4+12 z^4 a^{-2} +41 z^4-a^9 z^3+4 a^7 z^3+5 a^5 z^3-18 a^3 z^3-23 a z^3-4 z^3 a^{-1} +z^3 a^{-3} +2 a^8 z^2+a^6 z^2-16 a^4 z^2-27 a^2 z^2-2 z^2 a^{-2} -14 z^2-a^7 z-3 a^5 z+a^3 z+4 a z+z a^{-1} +2 a^4+3 a^2- a^{-2} +1 }[/math] |
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