K12a1047
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^4+3 q^3-7 q^2+12 q-16+21 q^{-1} -22 q^{-2} +21 q^{-3} -17 q^{-4} +12 q^{-5} -7 q^{-6} +3 q^{-7} - q^{-8} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^5-4 t^4+10 t^3-18 t^2+25 t-27+25 t^{-1} -18 t^{-2} +10 t^{-3} -4 t^{-4} + t^{-5} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^{10}+6 z^8+13 z^6+12 z^4+4 z^2+1 }[/math] |
| Determinant | 143 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ a^2 z^{10}-a^4 z^8+8 a^2 z^8-z^8-6 a^4 z^6+25 a^2 z^6-6 z^6-13 a^4 z^4+38 a^2 z^4-13 z^4-12 a^4 z^2+28 a^2 z^2-12 z^2-4 a^4+8 a^2-3 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 a^3 z^{11}+2 a z^{11}+5 a^4 z^{10}+10 a^2 z^{10}+5 z^{10}+6 a^5 z^9+3 a^3 z^9+2 a z^9+5 z^9 a^{-1} +6 a^6 z^8-11 a^4 z^8-37 a^2 z^8+3 z^8 a^{-2} -17 z^8+5 a^7 z^7-10 a^5 z^7-21 a^3 z^7-25 a z^7-18 z^7 a^{-1} +z^7 a^{-3} +3 a^8 z^6-8 a^6 z^6+18 a^4 z^6+60 a^2 z^6-11 z^6 a^{-2} +20 z^6+a^9 z^5-7 a^7 z^5+11 a^5 z^5+36 a^3 z^5+39 a z^5+18 z^5 a^{-1} -4 z^5 a^{-3} -5 a^8 z^4+4 a^6 z^4-19 a^4 z^4-57 a^2 z^4+10 z^4 a^{-2} -19 z^4-2 a^9 z^3+2 a^7 z^3-8 a^5 z^3-25 a^3 z^3-25 a z^3-8 z^3 a^{-1} +4 z^3 a^{-3} +2 a^8 z^2-2 a^6 z^2+13 a^4 z^2+33 a^2 z^2-3 z^2 a^{-2} +13 z^2+a^9 z+2 a^5 z+7 a^3 z+6 a z+z a^{-1} -z a^{-3} -4 a^4-8 a^2-3 }[/math] |
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