K12a1248
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^4+5 q^3-12 q^2+21 q-30+38 q^{-1} -40 q^{-2} +38 q^{-3} -31 q^{-4} +21 q^{-5} -12 q^{-6} +5 q^{-7} - q^{-8} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^5-6 t^4+17 t^3-32 t^2+46 t-51+46 t^{-1} -32 t^{-2} +17 t^{-3} -6 t^{-4} + t^{-5} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^{10}+4 z^8+4 z^6+1 }[/math] |
| Determinant | 255 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ a^2 z^{10}-a^4 z^8+6 a^2 z^8-z^8-4 a^4 z^6+12 a^2 z^6-4 z^6-4 a^4 z^4+8 a^2 z^4-4 z^4+1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 4 a^3 z^{11}+4 a z^{11}+12 a^4 z^{10}+22 a^2 z^{10}+10 z^{10}+18 a^5 z^9+22 a^3 z^9+14 a z^9+10 z^9 a^{-1} +18 a^6 z^8-a^4 z^8-43 a^2 z^8+5 z^8 a^{-2} -19 z^8+12 a^7 z^7-20 a^5 z^7-61 a^3 z^7-57 a z^7-27 z^7 a^{-1} +z^7 a^{-3} +5 a^8 z^6-24 a^6 z^6-30 a^4 z^6+12 a^2 z^6-13 z^6 a^{-2} +a^9 z^5-13 a^7 z^5-2 a^5 z^5+38 a^3 z^5+48 a z^5+20 z^5 a^{-1} -2 z^5 a^{-3} -3 a^8 z^4+10 a^6 z^4+22 a^4 z^4+11 a^2 z^4+9 z^4 a^{-2} +11 z^4+4 a^7 z^3+6 a^5 z^3-5 a^3 z^3-11 a z^3-3 z^3 a^{-1} +z^3 a^{-3} -a^6 z^2-4 a^4 z^2-6 a^2 z^2-z^2 a^{-2} -4 z^2+1 }[/math] |
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